Springer, 2014. — 257 p. — ISBN: 3642315429. This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. Riemann Surfaces Smooth and Noded Riemann Surfaces Riemann Surfaces and Hyperbolic Geometry The...
Princeton University Press , 2016 - 618 p. The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by...
2nd edition. — Springer, 2003 — 656 p. The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism,...
Cham: Springer, 2022. — 341 p. This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this...
IOP Publishing Ltd, 1997. — 306 p. The aim of this textbook is to provide the reader with an elementary introduction to fractal geometry and chaotic dynamics. These are subjects which have attracted immense interest throughout the whole range of numerate disciplines, including science, engineering, medicine, economics, and social science, to name but a few. The book may be used...
Dover Publications, 2012. — 420 p. — (Dover Books on Mathematics). — ISBN 978-0486498514. This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text...
10th Edition. — Arihant Prakashan, 2018. — 288 p. — (Skills in Mathematics for JEE MAIN & ADVANCED). — ISBN: 9312146939. Skills in Mathematics series of books for JEE Main and Advanced that serve as the comprehensive textbook, to covers all types and formats of questions with Remarks and Detailed explanations in sync with the latest pattern of JEE exam. Vector and 3D Geometry...
Cambridge: Cambridge University Press, 2020. — 768 p. Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research...
Springer, 2001. — 389 p. Japanese Conference, JCDCG 2000, Tokyo, Japan, November 22-25, 2000, Revised Papers. The Japan Conference on Discrete and Computational Geometry (JCDCG) has been held annually since 1997. One of the goals of this conference series is to bring together Japanese researchers from both academia and industry with researchers in these fields from abroad to...
Springer, 2015. — 434 p. — ISBN: 978-4-431-55841-5. This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians,...
Paris: European Mathematical Society, 2019. — 477 p. This book consists of a series of self-contained essays in non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski, Hermitian geometries, and some axiomatically defined geometries. Some of these essays deal...
Springer, 2019. — 95 p. — (SpringerBriefs in Mathematics). — ISBN: 3030053113. Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book...
Germany: Springer-Verlag Berlin Heidelberg, 2005. - 542 p. This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method....
Springer, 2016. — 594 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-319-24335-1. This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the...
Springer, 2015. - 321s. - ISBN: 978-3-662-45460-2 Dieses Buch handelt von 20 geometrischen Figuren (Icons), die eine wichtige Rolle bei der Veranschaulichung mathematischer Beweise spielen. Alsina und Nelsen untersuchen die Mathematik, die hinter diesen Figuren steckt und die sich aus ihnen ableiten lässt. Jedem in diesem Buch behandelten Icons ist ein eigenes Kapitel gewidmet,...
Cambridge University Press, 2022. — 417 p. — (London Mathematical Society Lecture Note Series, Series Number 472). — ISBN-13 9781108792509. Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic...
Cambridge University Press, 2022. — 394 p. — (London Mathematical Society Lecture Note Series, Series Number 473). — ISBN-13 9781108877855. Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic...
New York: Springer, 2016. — 373 p. — (Applied Mathematical Sciences, 194). — ISBN: 978-4-431-55977-1, 978-4-431-55978-8. Introduces information geometry intuitively to readers without knowledge of differential geometry Includes hot topics of applications to machine learning, signal processing, neural networks, and optimization Applies information geometry to statistical...
Springer-Verlag, 2018. — 460 p. — (Bolyai Society Mathematical Studies 27). — ISBN: 978-3-662-57412-6. This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and...
Belgrade (Serbia): Faculty of Mathematics, 2023. - 235 p. This book is meant to be a monograph on Osserman manifolds and brings together a large number of results published by the author in this topic. In order for as many readers as possible to follow these results, the book also contains a detailed introduction to smooth manifolds , as well as the basics of Riemannian and...
American Mathematical Society, 2020. — 791 p. — (Graduate Studies in Mathematics 206). — ISBN: 9781470455965. Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve...
Springer, 2017. — 262 p. — (Springer INdAM Series 21). — ISBN: 978-3-319-62913-1. This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the...
Boston: Kluwer Academic Publishers, 2003. — 740 p. Finsler geometry is the most general among those geometries which satisfy certain highly natural conditions. … In the last fifty years many papers and more books appeared on Finsler geometry. So it became difficult to obtain a good overlook on the subject. The present Handbook aims to fill this gap. … The authors wrote well...
Boston: Kluwer Academic Publishers, 2003. — 718 p. Finsler geometry is the most general among those geometries which satisfy certain highly natural conditions. … In the last fifty years many papers and more books appeared on Finsler geometry. So it became difficult to obtain a good overlook on the subject. The present Handbook aims to fill this gap. … The authors wrote well...
The Mathematical Association of America, 2013. — 520 p. — (Dolciani mathematical expositions 47). — ISBN: 978-0-88385-354-2, 978-1-61444-210-3. New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon...
Cambridge: Cambridge University Press, 2017. — 378 p. The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten...
Dover Publications, 2010. - 272 pages.
Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition....
Dover Publications, 2016. — 214 p. — ISBN: 978-0-486-80920-5, 0-486-80920-X. It’s hard for me to fathom that it’s been close to forty years ago since my early graduate school days, when I first encountered Emil Artin; I wonder if he’s as big a player now as he was then. I’m inclined to think not, given that many of the books he was known for now find themselves in competition...
Berlin: Springer, 2008. - 262p. This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a...
Springer, 2002. - 357 pages.
Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michèle Audin, professor at the university of Strasbourg has written a book allowing them to remedy this situation and, and starting from linear algebra extend their knowledge of affine, euclidian and projective geometry, conic and quadric...
Singapore: World Scientific Publishing Company, 2013. — 345 p. Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of...
Springer, 2017. — 411 p. — ISBN: 978-3-319-56477-7 The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both...
Springer, 2018. — 450 p. — (Springer Proceedings in Mathematics & Statistics). – ISBN: 978-3-319-97797-3. Information Geometry and its Applications, which was held on June 12–17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari’s 80th birthday and was organized by the Czech Academy of Sciences’ Institute of Information Theory and Automation. The...
Springer International Publishing AG, 2017. — 411 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 64) — ISBN: 3319564773. The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory,...
UK, USA: World Scientific, 2019. — 235 p. — ISBN10: 9814525650. Fractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the...
Springer, 2024. - 492 p. - (UNITEXT, 158). - ISBN 3031514130. This is an introductory textbook on geometry (affine, Euclidean and projective) suitable for any undergraduate or first-year graduate course in mathematics and physics . In particular, several parts of the first ten chapters can be used in a course of linear algebra, affine and Euclidean geometry by students of some...
Springer, 2012. — 330 p. This book reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. Features: presents an overview of the underlying mathematical theory, covering vector spaces, metric space, affine spaces, differential geometry, and finite difference...
Singapore: Imperial College Press. – 2007. – 521 p. (Imperial College Press Advanced Texts in Mathematics – Vol. 1). This book is divided into two parts. The first part is about Sign-Changing Yamabe-type problems. A Morse Lemma at infinity, under reasonable basic conjectures, is proved for such problems. This work is an attempt to define a new area of research for nonlinear...
Cambridge: The University Press, 1922. — 196 p.
Abstract Geometry
Propositions of Incidence
The correspondence of the points of two lines. Pappus' theorem
Introduction of algebraic symbols
Real Geometry
The Propositions of Incidence. Introduction of a plane, and of a space
The extension of the Real Geometry by means of Postulated Elements
A deduction of Pappus'...
Cambridge: The University Press, 1922. — 262 p.
Preliminary
General properties of conics
Properties relative to two points of reference
The equation of a line, and of a conic
Restriction of the algebraic symbols. The distinction of real and imaginary elements
Properties relative to an absolute conic. The notion of distance. Non-Euclidean geometry
Note I. On...
Cambridge: The University Press, 1923. — 228 p. Introduction to the theory of quadric surfaces Relations with a fixed conic. Spheres, confocal surfaces; quadrics through the intersection of two general quadrics Cubic curves in space. The intersection of two or more quadrics The general cubic surface. Introductory theorems
Cambridge: The University Press, 1925. — 250 p. Introductory. Relations of the geometry of two, three, four and five dimensions Hart's theorem, for circles in a plane, or for sections of a quadric The plane quartic curve with two double points A particular figure in space of four dimensions A figure of fifteen lines and points, in space of four dimensions; and associated loci A...
Cambridge: The University Press, 1933. — 247 p. Introductory account of rational and elliptic curves The elimination of the multiple points of a plane curve The branches of an algebraic curve; the order of a rational function; Abel's theorem The genus of a curve. Fundamentals of the theory of linear series The periods of algebraic integrals. Loops in a plane. Riemann surfaces The...
Cambridge: The University Press, 1933. — 308 p. Algebraic correspondence Schubert's calculus. Multiple correspondence Transformations and involutions for the most part in a plane Preliminary properties of surfaces in three and four dimensions Introduction to the theory of the invariants of birational transformation of a surface, particularly in space of three dimensions Surfaces...
New York: Springer, 2016. — 534 p. This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and...
Springer, 2015. — 339 p.
This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each...
Birkhauser, 1995. — 250 p.
Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between...
Birkhauser, 2000. — 286 p.
The second conference on Fractal Geometry and Stochastics was held at Greifs wald/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the...
Birkhauser, 2009. — 292 p.
Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to...
Birkhauser, 2004. — 264 p.
Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As...
Springer Basel, 2013. — 62 p.
The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important.
Fractal Symmetry of Protein Exterior investigates the diverse facets of the various scales at which we describe protein biophysical and...
Springer, 2021. — 466 p. — ISBN 978-3-030-77956-6. Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles...
Manual. — 4ª Edição. — Sociedade brasileira de matemática, 1995. — 142 p. — (Coleção do professor de matemática). — ISBN 85-85818-02-6. Este livro dá ao professor uma visão ampliada do que ele ensina em sala de aula. O autor mostra a geometria euclidiana plana de um ponto de vista que vai além dos tópicos do ensino básico e médio. A obra pode ser utilizada na disciplina de...
Springer, 2012. - 338 Pages. ISBN: 3642309631. 2nd edition
Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number...
Springer, 2010. - 311 Pages.
Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a...
Cambridge University Press, 2006. — 464 p. The chaos game. Attractors of iterated function systems. Another chaos game. Codes, metrics and topologies. Points and spaces. Functions, mappings and transformations. Addresses and code spaces. Metric spaces. Metrics on code space. Cauchy sequences, limits and continuity. Topological spaces. Important basic topologies. Some key...
2nd ed. — Morgan Kaufmann, 2000. — 534 p. This volume is the second edition of the highly successful Fractals Everywhere. The Focus of this text is how fractal geometry can be used to model real objects in the physical world. This edition of Fractals Everywhere is the most up-to-date fractal textbook available today. Fractals Everywhere may be supplemented by Michael F....
Horwood Publishing, 2001. - 225 Pages. ISBN: 1898563691
This book addresses a neglected mathematical area where basic geometry underpins undergraduate and graduate courses. Its interdisciplinary portfolio of applications includes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural...
2nd ed. — Woodhead Publishing, 2016. — 200 p. — ISBN: 0128050667, 9780128050668, 9780128050675, 0128050675. Geometry with Trigonometry Second Edition is a second course in plane Euclidean geometry, second in the sense that many of its basic concepts will have been dealt with at school, less precisely. It gets underway with a large section of pure geometry in Chapters 2 to 5...
Imperial College Press, 2011. - 328 pages. This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines. The integration of mathematics with physics, as well as...
Springer, 2008. — 197 p. — (Springer Monographs in Mathematics). — ISBN: 978-0-387-76364-4. This book is a monograph on unitals embedded in finite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are...
Academic Press, 1994. - 432 Pages. Fractal Cities is the pioneering study of the development and use of fractal geometry for understanding and planning the physical form of cities, showing how this geometry enables cities to be simulated throughcomputer graphics. The book explains how the structure of cities evolve in ways which at first sight may appear irregular, but when...
Springer, 2020. — XVI, 809 p. — ISBN: 978-3-030-30294-8; ISBN: 978-3-030-30293-1. Provides a self-contained and constructive approach to noncommutative differential geometry, which connects to the earlier approach to noncommutative geometry of Alain Connes in a complementary way Contains a wide range of examples drawn from quantum groups, algebra and mathematical physics...
Berlin: Springer, 1992. — 343 p. In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as...
Birkhauser, 2012. - 326 Pages. ISBN: 3034804199 The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2 It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for...
Springer, 2017. — 203 p. Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that...
Springer, 2020. — 500 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-030-56657-9. This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both...
3rd edition. — Springer, 2008. — 398 p. This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient...
Springer, 2007 — 824 p.
This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field.
Springer, 2009. - 446 pages. Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern...
Springer, 2009. — 416 pages. ISBN: 3540170154 This is the second of a two-volume textbook that provides a very readable and lively presentation of large parts of geometry in the classical sense. For each topic the author presents a theorem that is esthetically pleasing and easily stated, although the proof may be quite hard and concealed. Yet another strong trait of the book is...
Springer, 2010. - 860 pages.
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of...
Springer, 2018. — 187 p. — (Compact Textbooks in Mathematics). — ISBN: 978-3-030-01776-7. The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from...
N.-Y.: Marcel Dekker, 2003. — 486 p. — (Monographs and Textbooks in Pure and Applied Mathematics 253). — ISBN: 0-8247-0968-3. Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special...
Springer, 2010. - 166 pages.
This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research...
Springer International Publishing AG, 2018. — 125 p. — (Springer INdAM Series 25). — ISBN: 3319718339. This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent...
Academic Press Inc., 1964. — 287 p. Our purpose in writing this book is to put material which we found stimulating and interesting as graduate students into form. It is intended for individual study and for use as a text for graduate level courses such as the one from which this material stems, given by Professor W. Ambrose at MIT in 1958-1959. Previously the material had been...
Horwood Publishing, 2002. — 245 p. International authorities from Canada, Denmark, England, Germany, Russia and South Africa focus on research on fractal geometry and the best practices in software, theoretical mathematical algorithms, and analysis. They address the rich panoply of manifold applications of fractal geometry available for study and research in science and...
London: Dover Publications, 2017. — 208 p. Elegant and original, this exposition explores the foundations and development of both Euclidean and non-Euclidean geometry, particularly the postulational geometry of planes. Emphasis is placed upon the coordination of affine and projective planes as well as the basic unity of algebra and geometry. Geared toward undergraduate and...
Springer, 2013. — 323 p. — ISBN: 978-1-4614-6481-5. This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral...
Berlin: Springer, 1989. — 190 p. Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane...
Chicago: The Open Court Publishing Company, 1912. – 268 p. Authorised English translation with additional appendices by H. Carslaw with an introduction by F. Enriques. Translator’s Preface Author’s Preface The Attempts to prove Euclid’s Parallel Postulate. The Forerunners of Non-Euclidean Geometry The Founders of Non-Euclidean Geometry The Founders of Non-Euclidean Geometry...
Dover Publications Inc., 1958. — 265 p. + supplement. Bonola’s Non-Euclidean Geometry is an elementary historical and critical study of the development of that subject. Based upon his article in Enriques’ collection of Monographs on Questions of Elementary Geometry', in its final form it still retains its elementary character, and only in the last chapter is a knowledge of more...
Springer, 2014. — 410 p. Geometric Trilogy 1. An Axiomatic Approach to Geometry Geometric Trilogy 2. An Algebraic Approach to Geometry Geometric Trilogy 3. An Axiomatic Approach to Geometry The reader is invited to immerse himself in a love story which has been unfolding for 35 centuries: the love story between mathematicians and geometry. In addition to accompanying the reader up...
Springer, 2014. — 440 p. Geometric Trilogy 1. An Axiomatic Approach to Geometry Geometric Trilogy 2. An Algebraic Approach to Geometry Geometric Trilogy 3. An Axiomatic Approach to Geometry The reader is invited to immerse himself in a love story which has been unfolding for 35 centuries: the love story between mathematicians and geometry. In addition to accompanying the reader up...
Springer, 2014. — 462 p. Geometric Trilogy 1. An Axiomatic Approach to Geometry Geometric Trilogy 2. An Algebraic Approach to Geometry Geometric Trilogy 3. An Axiomatic Approach to Geometry The reader is invited to immerse himself in a love story which has been unfolding for 35 centuries: the love story between mathematicians and geometry. In addition to accompanying the reader up...
Springer, 2014. — 462 p. — ISBN 978-3-319-01735-8. This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter...
Springer Science+ Business Media, LLC, 2010. — 167 p. — (Universitext) — ISBN: 0387790659 Starting with basic principles, this book provides a comprehensive classification of the various types of finite reflection groups and describes their underlying geometric properties. Numerous exercises at various levels of difficulty are included. Mirrors and Reflections presents an...
Dover Publications, 2018. — 464 р. — ISBN: 9780486828091. Dover unabridged and slightly corrected republication of the edition originally published by the North-Holland Publishing Co., Amsterdam, and Interscience Publishers, New York, 1960. In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the...
Basel: Birkhäuser, 2020. — 395 p. This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer...
Natick, Massachusetts: AK Peters, 2010. — 243 p. — ISBN10: 1568814267 — ISBN13: 9781568814261 Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex...
Springer Science+Business Media, 1996. — 195 Pages. ISBN: 1461269180 Fractal geometry is the formal study of mathematical shapes that display a progression of never-ending, self-similar, meandering detail from large to small scales. It has the descriptive power to capture, explain, and enhance one's appreciation of and control over complex diversity. Natural shapes and rhythms,...
Student Edition. Publisher: Glencoe/McGraw-Hill, 2007. - 960 pages.
Glencoe Geometry is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today’s high-stakes assessments.
Oxford: Oxford University Press, 2007. — 620 p. Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an algebraic variety. The book is divided into three parts. The first five chapters carefully prepare the stage for the proper introduction...
Springer International Publishing AG, 2017. — 185 p. — (Springer INdAM Series 26). — ISBN: 3319731254. The book collects the most relevant outcomes from the INdAM Workshop "Geometric Function Theory in Higher Dimension" held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same...
2nd edition. — Cambridge: Cambridge University Press, 2012. — 587 p. This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective,...
Springer, 2006. — 507 p. — ISBN-13 978-0387238159. Although discrete geometry has a rich history extending more than 150 years, it abounds in open problems that even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones,...
Basel: Birkhäuser, 2012. — 721 p. — (Modern Birkhäuser Classics). — ISBN: 303480492X, 9783034804929. In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising...
Berlin: de Gruyter, 1996. — 384 p. Foreword Introduction Basic algorithms in real algebraic geometry and their complexity: from Sturm’s theorem to the existential theory of reals Introduction Real closed fields Definition and first examples of real closed fields Cauchy index and real root counting Real root counting Sylvester sequence Subresultants and remainders...
San Rafael: Morgan & Claypool, 2009. — 177 p. Basic Algebraic Notions A Historical Perspective in the Algebraic Context Algebraic Preliminaries Jordan Normal Form Indefinite Geometry Algebraic Curvature Tensors Hermitian and Para-Hermitian Geometry The Jacobi and Skew Symmetric Curvature Operators Sectional, Ricci, Scalar, and Weyl Curvature Curvature Decompositions...
Springer, 2004. — 473 p. Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization. Experts in both fields from all over the world have been...
Springer, 2013. — 596 p. — ISBN: 3642344526, 9783642344527. This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on...
European Mathematical Society, Switzerland, 2007. — 213 p. — (EMS Monographs in Mathematics) — ISBN: 3037190361 Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely...
Springer, 2008. — 240 p. — (Lecture Notes in Mathematics 1764). — ISBN: 978-3-540-42195-5. The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex...
Providence: American Mathematical Society, 2017. — 119 p. This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and...
Birkhäuser, 1992. - 315 pages. Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is...
Springer International Publishing, Switzerland, 2014. — 445 p. — (Lecture Notes of the Unione Matematica Italiana 15) — ISBN: 3319065130 The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In...
North-Holland Publishing Company, 1975. — 181 pages. — (North-Holland Publishing Library, 9). — ISBN: 0-7204-2461-5. In this book we study complete Riemannian manifolds by developing techniques for comparing the geometry of a general manifold M with that of a simply connected model spaceM_H of constant curvature H. A typical conclusion is that M retains particular geometrical...
New York: Springer, 2020. — 468 p. The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each...
Springer, 2020. — 615 p. — (Progress in Mathematics 333). — ISBN: 978-3-030-34952-3. This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and...
Springer, 2015. — 342 p. — ISBN: 3319120980, 9783319120980
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData. The author investigates digital...
Springer, 2019. — 428 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete 69). — ISBN: 978-3-319-95890-3. This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep...
Chapman and Hall/CRC, 2012, ISBN: 1584887303, 410 pages. Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors...
Springer International Publishing AG, 2017. — 341 p. — (Springer INdAM Series 23) — ISBN: 978-3-319-67518-3. The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic...
Springer, 2019. — 635 p. — (Trends in Mathematics). — ISBN: 978-3-319-94219-3. This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains...
Princeton University Press, 2017. — 456 p. — ISBN10: 0691158665. Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincare, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key...
Providence: American Mathematical Society, 2017. — 442 p. Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and...
Springer, 2020. — 204 p. — (Springer INdAM Series 39). — ISBN: 978-3-030-37113-5. This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same...
New York: Springer, 2018. — 349 p. This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of...
Published Online. — 1994 — 654 p. This book is the English version of the French "Geometrie non commutative" published by InterEditions Paris (1990). Noncommutative Spaces and Measure Theory Heisenberg and the Noncommutative Algebra of Physical Quantities Statistical State of a Macroscopic System and Quantum Statistical Mechanics Modular Theory and the Classification of Factors...
Constable and Co, 1914. - 524 pages.
Classic, well-thought-out examination of the function of the spiral, or helix, in both nature and art. Demonstrates how spiral is fundamental to structure of shells, leaves, horns, human body, drawings of Leonardo, Leaning Tower of Pisa, more. 426 illustrations.
A fascinating and comprehensive investigation into the perfect geometry of...
12da edición. — Editores Asociados., 2000. — 408 p. Nociones preliminares Representación del punto Representación de la recta Representación del plano Intersección de planos y de rectas con planos Paralelismo y perpendicularidad entre planos, y entre rectas y planos Métodos de la geometría descriptiva: método de los cambios de planos, método de los giros, método de los...
2da ed. — Barreiro y Ramos S.A., 1970. — 195 p. Nociones sobre conjuntos Preliminares Partes de un conjunto Operaciones entre dos conjuntos Introducción Idea de punto, recta y plano Semirrecta Segmentos Igualdad y desigualdad de segmentos Adición y sustracción de segmentos. Definiciones y propiedades Circunferencia Posiciones relativas de una recta y una circunferencia Semiplano...
Springer, 2003. — 333 p. — (Advances in Mathematics 05). — ISBN: 978-1-4419-5245-5. This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6)...
Boca Raton: CRC Press, 2021. — 350 p. — ISBN 9780367468644. Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe ? What is a...
The Mathematical Association of America, 1967. — 210 p. — (New Mathematical Library 19). — ISBN: 978-0-88385-619-2. Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational...
2nd Edition. — Wiley, 1989. — 243 p. — ISBN: 978-0-471-50458-0. This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to...
Amsterdam: Springer, 2001. — 446 p. It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting...
Springer, 2024. — 498 p. This book presents a comprehensive set of methods for quantifying geometric quantities such as the volume of a tumor, the total surface area of the alveoli in a lung, the length of plant roots, or of blood vessels, the number of neurons in a brain compartment, the connectivity number of trabecular bone, the mean size of grains in a rock, etc.. The...
Budapest: Typotex Publishing House, 2014. — 354 p. - (Series of Lecture Notes and Workbooks for Teaching Undergraduate Mathematics). The aim of this textbook is to give an introduction to differential geometry. It is based on the lectures given by the author at Eötvös Loránd University and at Budapest Semesters in Mathematics. In the first chapter, some preliminary definitions and...
Springer, 2021. — 864 p. — (Artificial Intelligence: Foundations, Theory, and Algorithms). — ISBN 978-3-030-63152-9. The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space,...
2nd ed. — Birkhäuser, 2019. — 238 p. — (Cornerstones). — ISBN: 3030165132. This textbook provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes...
Springer, 2013. — 211 p. — ISBN: 978-1-4614-8525-4. Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric...
Kluwer, 1990. — 536 p. Assembled here is a collection of articles presented at a NATO Advanced Study Institute held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing...
Clarendon Press, 1997. — 111 p. Fractal patterns have emerged in many contexts, but what exactly is a pattern? How can one make precise the structures lying within objects and the relationships between them? This book proposes new notions of coherent geometric structure to provide a fresh approach to this familiar field. It develops a new concept of self-similarity called "BPI"...
Scranton: International Textbook Co, 1917. — 310 p. The study of Geometry is a process of systematic and orderly reasoning rather than a matter of memory. The student is advised to study the principles and propositions stated until he understands them thoroughly and sees their relation one to another, and, when a proposition is accompanied by an explanation in small type, to...
Springer, 2024. — 273 p. Preface Acronyms Introduction Overview Nonpositively Curved Cube Complexes Polyhedral Preliminaries Right-Angled Spaces and Groups Coxeter Groups, Artin Groups, Buildings More on NPC Cube Complexes General Theory of Cube Complexes Hyperbolization Morse Theory and Bestvina–Brady Groups Complexes of Groups References Index
Springer, 2008. — 387 p. 370 illus. — 3rd ed. — ISBN: 3540779736, 9783540779742 This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all...
Springer International Publishing AG, 2016. — 380 p. — (Frontiers in Mathematics) — ISBN10: 3319438107 This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among...
Basel: Birkhäuser, 2006. — 268 p. Near polygons were introduced about 25 years ago and studied intensively in the 1980s. In recent years the subject has regained interest. This monograph gives an extensive overview of the basic theory of general near polygons. The first part of the book includes a discussion of the classes of dense near polygons, regular near polygons, and...
Wiley-Scrivener, 2022. — 504 p. — (Modern Mathematics in Computer Science). — ISBN 1119795621. This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting....
Key Curriculum Press, USA, Michael de Villiers, 2009. — 219 p. — ISBN: 0557102952. This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been...
N.Y., USA: Dover Publications, Inc., 2008. — 207 p. — (Dover Books on Mathematics). — ISBN: 0486466299. Introduction to the Geometry of Complex Numbers Roland Deaux, Howard Eves Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an...
Springer, 2013. — 411 p. — (Progress in Mathematics 304). — ISBN: 978-3-0348-0486-8. This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory...
New York, USA: Cambridge University Press, 2007. — 486 p. — ISBN13: 978-0-521-85757-4. How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Linkages Problem Classification and...
Princeton, New Jersey: Princeton University Press, 2011. — 270 p. Although geometry is as old as mathematics itself, discrete geometry only fully emerged in the twentieth century, and computational geometry was only christened in the late 1970s. The terms discrete and computational fit well together, as the geometry must be discretized in preparation for computations. Discrete...
Berlin: Springer, 2010. — 554 p. Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with...
Berlin: Springer, 2010. — 642 p. Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to...
Springer, 2005. — 218 p. The book fills a gap in the steadily expanding field of applying fractals to the earth science system. In this book the concept of fractal-scaling is applied to a variety of geophysical problems, illustrating what scaling laws really tell us and how they can used to solve various geophysical problems. Keeping in mind the broad range of readers...
Springer Science & Business Media, 2013. — 243 p. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be...
Cambridge: Cambridge University Press, 2016. — 314 p. Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fréchet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie...
Springer, 2009 — 434 p.
2nd edition.
This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the...
Springer, 2014. — 340 p. — ISBN10: 3319086340 This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate...
Springer, 2004. - 425 Pages.
Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from important topics in modern geometry.
Preface. Modern information technology allows most mathematicians unprecedented access to the research literature....
Oxford University Press, 1997 — 456 p.
The last ten years have seen rapid advances in the understanding of differentiable four-manifolds, not least of which has been the discovery of new 'exotic' manifolds. These results have had far-reaching consequences in geometry, topology, and mathematical physics, and have proven to be a mainspring of current mathematical research. This...
Springer Basel, 2014. — 352 p. — ISBN: 3034808429. This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original - the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of...
Moscú: Mir, 1987. — 378 p. Tradicionalmente, la teoría de homologías desempeña un papel fundamental en la exposición de los principios de la topología. A partir de H. Poincaré, quien fundó las bases de la topología, la teoría de homologías se considera como una base inicial de los métodos de la topología algebraica. En la teoría de homotopías sólo el grupo fundamental y los...
Utrecht University, 2004. — 42 p. Symplectic Linear Algebra Symplectic Forms Orthogonal Complements in the Dual Space Orthogonal Complements for a Bilinear Form Isotropic Subspaces Standard Form of the Sympctic Form The Lagrangian Grassmannian The Symplectic Linear Group Exterior Algebra Hermitian Forms Historical Remarks Exercises Symplectic Manifolds Definition The Cotangent...
Springer, 2019. — 140 p. — (Springer Briefs in Mathematics). — ISBN: 978-3-030-27226-5. This monograph could serve as the textbook for a graduate course on symplectic geometry. It has been used for this purpose in graduate courses taught in the Mathematics Department at the University of Toronto. This book evolved from the lecture notes for the graduate course on symplectic...
Springer, 2005 — 309 p. The book under review provides an introduction to the contemporary theory of compact complex manifolds, with a particular emphasis on Kähler manifolds in their various aspects and applications. As the author points out in the preface, the text is based on a two-semester course at the University of Cologne, Germany. Having been designed for third-year...
Издательство Addison-Wesley, 1971. — 184 p. — ISBN: 0201018519. This book is about one-to-one functions from the points of the plane onto the plane. Such transformations are applied to the study of geometry to bring a deeper understanding of congruence and similarity, and of the basic function concepts. Traditional geometry courses have placed geometry in a compartment quite...
Cham: Birkhäuser, 2022. — 119 p. This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov...
Springer, 2018. — 165 p. — (SpringerBriefs in Mathematical Physics 27). — ISBN: 978-3-319-94787-7. What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of...
Springer, 2014, ISBN: 3319059564, 110 pages. This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the...
Fractal Examples.
The Triadic Cantor Dust.
The Sierpi´nski Gasket.
A Space of Strings.
Turtle Graphics.
Sets Defined Recursively.
Number Systems.
*Remarks.
Metric Topology.
Metric Space.
Metric Structures.
Separable and Compact Spaces.
Uniform Convergence.
The Hausdorff Metric.
Metrics for Strings.
*Remarks.
Topological Dimension.
Zero-Dimensional Spaces....
Springer, 2020. — 826 p. — (Grundlehren der mathematischen Wissenschaften 355). — ISBN: 978-3-030-30293-1. This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute. This requires a reinvention of differential geometry that refers only to the coordinate algebra, now possibly noncommutative, rather than...
Moscú: Mir, 1984. — 508 p. El libro que ofrecemos es uno de los mejores manuales de análisis matemático. La exposición del material se realiza en forma Clara, pero rigurosa. La obra ha sido escrita por un pedagogo experto que en el transcurso de muchos atlas dio conferencias sobre las distintas partes del curso en el Instituto Físico — Técnico de Moscú. En la primera parte de...
Princeton University Press, 2016. — 183 p. This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or...
Princeton University Press, 1997. — 318 p. — (Princeton Landmarks in Mathematics and Physics). — ISBN: 0691023530. In his classic work of geometry, Euclid focused on the properties of flat surfaces. In the age of exploration, mapmakers such as Mercator had to concern themselves with the properties of spherical surfaces. The study of curved surfaces, or non-Euclidean geometry,...
Springer, 2020. — 592 p. — (RSME Springer Series 05). — ISBN: 978-3-030-48826-0. Mощный инструмент в геометрической теории представления This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are...
Springer, 1993. — 104 p. — ISBN: 9783642780547 This book appeared about ten years ago in Gennan. It started as notes for a course which I gave intermittently at the ETH over a number of years. Following repeated suggestions, this English translation was commissioned by Springer; they were most fortunate in finding translators whose mathemati cal stature, grasp of the language...
Cambridge University Press, 2018. — 242 p. — ISBN: 978-1-108-42391-5. This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are...
Cham: Birkhäuser, 2022. — 203 p. This monograph presents an approachable proof of Mirzakhani’s curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to rigorous proofs. This approach illuminates new and established results alike, and produces versatile...
Wiesbaden: Springer, 2022. — 168 p. This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of...
London: Stacey International, 1974. — 68 p. — ISBN 0950-3304-0X. This collection of theorems in plane geometry, some of which we believe to be new, illustrates that there may still be plenty of interesting theorems awaiting discovery. We derived a lot of enjoyment from evolving them (or, as it transpired in some cases, rediscovering them) and it is our sincere hope that the...
Rio de Janeiro: Daniel G. Fadel e Henrique N. Sá Earp, 2019. — 197 p. This book is an introduction to gauge theory in dimensions greater than . It is organised as a reader's guide to Gang Tian's landmark article Gauge theory and calibrated geometry, I, published in the Annals of Mathematics in 2000. Tian carried out to substantial lengths the programme outlined by Simon...
Foundations 1. mathematical background. Basic set theory. Functions and limits. Measures and mass distributions. Notes on probability theory. Notes and references. Exercises. Hausdorff measure and dimension. Hausdorff measure. Hausdorff dimension. Calculation of Hausdorff dimension—simple examples. *2.4 Equivalent definitions of Hausdorff dimension. *2.5 Finer definitions of...
Wiley. Chichester, UK. 3rd Edition. 2014. 400 pages. Includes references and index.
ISBN: 111994239X.
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own...
Chichester, West Sussex, John Willey & sons, 1979, 331 p. Department of Mathematics Cranfield Institute of Technology. This book deals with the mathematical techniques which have been developed in recent years for the representation, analysis and synthesis of "shape information" by computers. This area of mathematics is now assuming major importance in the manufacturing...
Springer Science + Business Media, LLC, 1988. — 305 p. — (Physics of Solids and Liquids) — ISBN: 9781489921260 This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of...
Oxford University Press, 2012. - 431 p. - This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated...
Springer, 2014. — 360 p. — (Springer Proceedings in Mathematics & Statistics 88). — ISBN: 978-3-662-43919-7. This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective...
Cambridge University Press, 2011. — 206 p. — (Encyclopedia of Mathematics and its Applications, Book 139). — ISBN: 1107031702, 9780521461931 Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and...
Society for Industrial and Applied Mathematics, 2009. - 213 Pages. Second Edition Mathematical symmetry and chaos come together to form striking, beautiful color images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns. The book, a richly illustrated blend of mathematics and art, was widely hailed in...
Berlin: Humboldt-Universität zu Berlin, 1993. — 267 S. Einen wichtigen Stellenwert in diesem Buch nehmen Betrachtungen zur Geschichte der Geometrie ein, wurde doch die Entwicklung der Mathematik durch diejenigen Gebiete der Geometrie, welche Gegenstand dieses Buches sind, maßgeblich geprägt. Über weite Strecken der Kapitel 2 und 3 erfolgt die Behandlung des Stoffes in Anlehnung...
2nd edition. — Berlin: de Gruyter, 2022. — 364 p. In the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. This volume examines many fundamental results in Geometry and Discrete Mathematics along with their proofs and their history. In the second edition we include a new chapter on Topological Data Analysis...
De Gruyter, 2018. — 284 p. — ISBN 9783110521450 3110521458. The first volume was called Algebra and Number Theory: A Selection of Highlights. This second volume is Geometry and Discrete Mathematics: A Selection of Highlights. This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to...
Springer, 2012, ISBN: 3642172822, 312 pages Arrangements of curves constitute fundamental structures that have been intensively studied in computational geometry. Arrangements have numerous applications in a wide range of areas – examples include geographic information systems, robot motion planning, statistics, computer-assisted surgery and molecular biology. Implementing...
Springer, 2008. — 409 p.
The flood of information through various computer networks such as the In ternet characterizes the world situation in which we live. Information worlds, often called virtual spaces and cyberspaces, have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of...
Boston: Birkhauser, 1998. — 268 p. Vector bundles arise in geometry in several contexts. One may remember from the study of smooth manifolds that the notion of tangent bundle inevitably appeared as a powerful tool of differential geometry. If the dimension of a manifold M is k then the dimension of the total space of the tangent bundle to M is twice as big. The first and simple...
New Haven: Yale University Press, 2016. — 526 p. Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia...
Marc Frantz, 1997. — 60 p. An undergraduate textbook devoted exclusively to relationships between mathematics and art, it is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a...
Princeton University Press, 2011. - 258 pages. An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written...
Cambridge: Cambridge University Press, 2019. — 287 p. Acknowledgements Theory Fractal Geometry and Dimension Theory The Emergence of Fractal Geometry Dimension Theory The Assouad Dimension The Assouad Dimension and a Simple Example A Word or Two on the Definition Some History Basic Properties: The Greatest of All Dimensions Some Variations on the Assouad Dimension The Lower...
Springer, 2003. — 303 p. — (Progress in Mathematics 218). — ISBN: 978-1-4612-6585-6. "… beginners will appreciate the numerous exercises and the gentle progression of the first four chapters, from the one-variable calculus on the projective line, through the algebraic study of general affinoid algebras, to the definition of general rigid varieties and their analytic reductions....
USA: ILQ, 2007. — 203 p. The Scientific Elements is an international book series, maybe with different subtitles. This series is devoted to the applications of Smarandache’s notions and to mathematical combinatorics. These are two heartening mathematical theories for sciences and can be applied to many fields. This book selects 12 papers for showing applications of...
Paris: European Mathematical Society, 2018. — 865 p. Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate’s rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich...
European Mathematical Society, Switzerland, 2017. — 787 p. — (EMS Monographs in Mathematics) — ISBN: 3037190361. Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate’s rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a...
Austin: University of Texas at Austin, 2010. — 33 s. Geometric transformations Representation Two-dimensional transformations Identity Scaling Reflection Shear Effect on unit square Rotation Linear transformations
2nd Edition. — Springer, 2011. — 707 p. — ISBN 978-1-4419-9961-0. This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine...
Philadelphia: University of Pennsylvania, 2020. — 580 p. The goal of differential geometry is to study the geometry and the topology of manifolds using techniques involving differentiation in one way or another. The pilars of differential geometry are: Riemannian metrics. Connections. Geodesics. Curvature. This book is written for a wide audience ranging from upper undergraduate...
Cambridge: Cambridge University Press, 2010. — 416 p. Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional...
Cham: Springer, 2022. — 591 p. This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches...
Author: LE Editors. Publisher: Learning Express, 2010. - 215 pages. Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with...
Chapman and Hall/CRC, 2021. — 397 p. This book introduces plane curves on time scales. They are deducted the Frenet equations for plane and space curves. In the book is presented the basic theory of surfaces on time scales. They are defined tangent plane, \sigma_1 and \sigma_2 tangent planes, normal, \sigma_1 and \sigma_2 normals to a surface. They are introduced differentiable...
The Mathematical Association of America, 1999. - 224 pages.
This book draws on geometric ideas from cultural activities from Subsaharan Africa, and demonstrates how they may be explored to develop mathematical reasoning from school level through to university standard. Paulus Gerdes provides a thoroughly illustrated and researched exploration of mathematical ideas, motifs and...
World Scientific Publishing, 2022. — 160 p. — ISBN-13 9789811253836. Вычислительная геометрия с независимыми и зависимыми неопределенностями This comprehensive compendium describes a parametric model and algorithmic theory to represent geometric entities with dependent uncertainties between them. The theory, named Linear Parametric Geometric Uncertainty Model (LPGUM), is an...
Berlin: Springer, 2016. — 496 p. — ISBN: 978-3-662-45449-7, 978-3-662-45450-3. This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries....
2nd Edition. — Springer, 2021. — 708 p. — ISBN 978-3-030-61397-6. This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology,...
Walter de Gruyter, 2024. — 249 p. — (Edition Angewandte). — ISBN 978-3-11-136523-7. This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains...
3rd ed. — Boca Raton: CRC Press, 2017. — 1950 p. — (Discrete Mathematics and Its Applications). — ISBN: 978-1-4987-1139-5. The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and...
2nd edition. — Chapman and Hall/CRC, 2004. — 1558 pages. — (The CRC Press series on discrete mathematics and its applications). — ISBN 1-58488-301-4. While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive...
Springer, 2008. — 652 p. While we were busy putting together the present collection of articles celebrating the twentieth birthday of our journal, Discrete & Computational Geometry, and, in a way, of the field that has become known under the same name, two more years have elapsed. There is no doubt that DCG has crossed the line between childhood and adulthood. By the mid-1980s...
Facts on File, 2009. — 342 p. Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There...
Birkhäuser, 2011. — 210 pp. Grand visions in mathematics can begin with simple observations. It is hardly more than a homework exercise to prove that what we nowadays call the Poincaré metric on the unit disc is invariant under the biholomorphic maps of the unit disc to itself. But this easily established fact, when combined with the (profound) uniformization theorem of...
Springer, 2019. — 569 p. — (Springer Monographs in Mathematics). — ISBN: 303003349X. Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry. The monograph suggests a unified...
London: Wiley, 2011. — 830 p. A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic...
Birkhauser Boston - 2006, 593 pages. Based on "Structures Mtriques des Varites Riemanninnes", edited by J. LaFontaine & P. Pansu. Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new...
Springer, 2023. — 348 p. — (Springer Undergraduate Mathematics Series). — ISBN 978-3-031-25408-6. Многообразия, векторные поля и дифференциальные формы: введение в дифференциальную геометрию This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and...
Springer, 2007. — xiv, 580 p. — (Grundlehren der mathematischen Wissenschaften, 336). — ISBN 978-3-540-71132-2. Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its...
2nd Edition. — Springer,1977. — 208 p. — (Graduate Texts in Mathematics 49). — ISBN: 978-1-4419-2806-1. This is essentially a book on linear algebra. But the approach is somewhat unusual in that we emphasise throughout the geometric aspect of the subject. The material is suitable for a course on linear algebra for mathe matics majors at North American Universities in their...
Higer Education Press, 2008. — 295 p. Computational conformal geometry is an emerging inter-disciplinary field, with applications to algebraic topology, differential geometry and Riemann surface theories applied to geometric modeling, computer graphics, computer vision, medical imaging, visualization, scientific computation, and many other engineering fields. This volume...
Springer, 2005. — 175 p. — (Lecture Notes in Mathematics 1870). — ISBN-13 978-3-540-28800-8. Геометрия пространств и смежные вопросы Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The...
Springer Spektrum, 2016. — 228 p. — ISBN: 978-3-662-53034-4. Dieses Buch nimmt Sie mit auf eine Entdeckungsreise durch die Welt der klassischen Geometrie: Beginnend beim Satz von Thales und den Apolloniuskreisen führt die Reise über Steiner'sche Kreisketten bis in die Welt der Kegelschnitte. Dabei werden verborgene Zusammenhänge aufgedeckt und Perlen der Elementargeometrie...
Cambridge University Press, 2012. — xiv, 271. — (London Mathematical Society Lecture Note Series, 400). — ISBN: 978-0-521-61770-3. True PDF he 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that...
Independent Publishing, 2019. — 68 p. Well-dimensioned numbers vanquish the mystery of imaginary ones, like so: Various kinds have just the right elbow room to perform various kinds of dimensioned quarter turns. Two quarter turns is a half turn, direction reversal, multiplication by -1. ¿That doesn't seem mysterious, does it?
Springer, 2000. — 536 p. — (Undergraduate Texts in Mathematics). — ISBN: 978-1-4419-3145-0. In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's...
Self-published, 2017. — 601 p. Elementary geometry is the stepping stone to more advance mathematical subjects. It is needed to understand many components of physics, chemistry and engineering. Even the biological sciences require an understanding of geometry, especially biochemistry. In fact, more and more scientific disciplines have come to rely on mathematics of some kind which...
Springer, 2011. — 316 p. — ISBN: 978-1-4419-6054-2. In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds―hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support...
2nd ed. — Birkhäuser, 1999. — 197 p. The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition. Many examples of the explicit inversion formulas and range theorems have been added, and the group-theoretic viewpoint emphasized. For example, the integral geometric viewpoint of the...
Walter de Gruyter, 2007. — 177 p. — ISBN: 3110190923
The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes...
Springer, 2016. — 247 S. — ISBN: 978-3-662-47205-7. Das vorliegende Lehrbuch entwickelt Geometrie für die Studierenden des Lehramts Primarstufe von fünf Leitvorstellungen aus: Geometrie hilft uns beim Wahrnehmen räumlicher Zusammenhänge und bei der Orientierung im Raum, sie dient dem Erfassen von Formen und dem (künstlerischen) Gestalten von Mustern. Zudem beschäftigt sie sich...
New York: Pearson, 2004. — 405 p. The formal expression of "straightness" is a part of differential geometry and is a very difficult formal area of mathematics. However, the concept of "straight," an often used part of ordinary language, is generally used and experienced by humans starting at a very early age. This book will lead the reader on an exploration of the notion of...
Beograd: Naučno Delo, 1957. — 232 s. Ovaj novi otisak Hilbertovih Osnovi geometrije nije neka prava nova prerada. Upravo uinjene su samo neke ispravke i manje dopune. U dopuni I su skupljene neke zavisnosti u sistemu aksioma realnih brojeva, ranije navedene u dodatku VI. Dopuna III je u sutini p onavljanje jedne dopune do datka II u p etom izdanju, ko ja se o dnosi na izvo...
El. edition - La Salle (IL.): The Open Court Publishing Company, 1950. — 97 p. The material contained in the following translation was given in substance by Professor Hilbert as a course of lectures on euclidean geometry at the University of Göttingen during the winter semester of 1898 – 1899. The results of his investigation were re-arranged and put into the form in which they...
Springer, 2012. — 742 p. — (Springer Monographs in Mathematics). — ISBN: 0387847936. This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn...
Linfield College, 2018. — 217 p. Geometry with an Introduction to Cosmic Topology approaches geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe ? Does the universe have an edge ? Is it infinitely big ? This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate...
Springer, 2019. — 301 p. — (Lecture Notes of the Unione Matematica Italiana 26). — ISBN: 978-3-030-18637-1. Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and...
Springer, 2021. — 281 p. — (Springer Proceedings in Mathematics & Statistics, 349). — ISBN 978-3-030-68540-9. This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and...
Springer, 2010. - 551 pages.
This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of future mathematics teachers. One of my goals for this book is to open up for the dynamic character of geometry as such, and to extend...
Chapman and Hall/CRC, 2024. — 147 p. The main focus of this book is disseminating research results regarding the pencil of ellipses inscribing arbitrary convex quadrilaterals. In particular, the author proves that there is a unique ellipse of maximal area, EA, and a unique ellipse of minimal eccentricity, EI, inscribed in Q. Similar results are also proven for ellipses passing...
Springer, 2020. — 299 p. — (Graduate Texts in Mathematics, 286). — ISBN: 3030501795. This book provides a self-contained introduction to convex geometry in Euclidean space . After covering the basic concepts and results, it develops Brunn–Minkowski theory , with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the...
2nd Edition. — Springer, 2020. — 128 p. — (Advanced Courses in Mathematics CRM Barcelona). — ISBN: 978-3-030-55292-3. This book contains a clear exposition of two contemporary topics in modern differential geometry: Distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature The...
2nd ed. — Springer, 2003. — 510 p. — ISBN: 0387954902, 9780387954905. This book is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. The first part, which grew out of Tate's Haverford lectures, covers the elementary arithmetic theory of elliptic curves over the rationals. The next two chapters recast the arguments...
Springer, 2005. — 321 p. — ISBN: 3-540-21290-6. Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
New York: Springer, 2004. — 321 p. Complex geometry is a highly attractive branch of modern mathematics that has witnessed many years of active and successful research and that has recently obtained new impetus from physicists' interest in questions related to mirror symmetry. Due to its interactions with various other fields (differential, algebraic, and arithmetic geometry,...
Boca Raton: CRC Press, 2017. — 545 p. Features Second edition of a successful textbook for the first undergraduate course Every major concept is introduced in its historical context and connects the idea with real life Focus on experimentation Projects enhance student learning All major software programs can be used; free software from author This text promotes student...
New York: McGraw-Hill, 2005. — 478 p. Geometry with Geometry Explorer combines a discovery-based geometry text with powerful integrated geometry software. This combination allows for the deep exploration of topics that would be impossible without well-integrated technology, such as hyperbolic geometry, and encourages the kind of experimentation and self-discovery needed for...
Springer, 2020. — 225 p. — (Texts & Monographs in Symbolic Computation). — ISBN: 978-3-319-59188-9. In this book, origami is treated as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers. Focusing on how classical and modern geometrical problems are solved by means of origami, the book explains the methods not only...
Cambridge: Cambridge University Press, 2022. — 178 p. The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and...
Princeton University Press , 2016 - 269 p. This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to...
Springer, 2009. - 554 pages. This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving process, and focusing on parallel coordinates. The barrier, imposed by our three-dimensional habitation and perceptual experience, has been breached by this innovative and versatile methodology. The accurate visualization...
Springer International Publishing AG, 2018. — 318 p. — ISBN: 3319753304. This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental...
Cambridge University Press, 2018. — 471 p. — ISBN: 978-1-107-10340-5. Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the...
Chapman and Hall/CRC, 2023. — 356 p. — ISBN: 978-1-032-34916-9. Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily...
Springer, 2017. — 702 p. — (Universitext). — ISBN: 978-3-319-61859-3. This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic...
Springer. Heidelberg Dordrecht London New York. 6th edition. 2011. 630 pages. Includes index. ISBN: 3642212972. This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work...
Boca Raton: CRC Press, 2015. — 206 p. — ISBN: 1482259508, 9781482259506. Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann, and Clifford. It shows how to describe and compute geometry for 3D modeling applications in computer...
World Scientific Publishing Company, 2002. - 470 pages.
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in "Mathematics, Chemistry, and Astronomy - Professional and Reference" in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in...
Berlin/Boston, Germany: Walter de Gruyter GmbH, 2017. — 147 p. — ISBN10: 311053147X. This unique book's subject is meanders (connected non-self-intersecting planar curves) in the context of dynamical systems. Supplementing the rigorous results with a large number of insightful figures, the author presents issues such as the connectivity and collapse of meanders as well as...
World Scientific Publishing Co. Pte. Ltd., 2017. — 255 p. — ISBN10: 9814635367 This book provides comprehensive analysis of dynamical systems in tropical geometry, which include the author's significant discoveries and pioneering contributions. Tropical geometry is a kind of dynamical scale transform which connects real rational dynamics with piecewise linear one presented by...
Second Edition. — VCH, 1994. — 453 Pages. — ISBN: 3527290788. Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the descriptive power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. The second edition of this successful...
Yale University, 1975. - 139 pages. ISBN: 0883856042
Anybody who liked his first geometry course will enjoy the simply stated geometric problems about maximum and minimum lenghs and areas in this book. Many of these already fascinated the greeks, for example the problem of of enclosing the largest possible area by a fence of given length, and some were solved long ago; but...
Mathematical Association of America, 2012. — 205 pages. ISBN: 0883853531. This is an informal and accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry. There is a unifying theme to the book: give curves enough living space and beautiful theorems will follow. This book provides the reader with a solid intuition for the...
Philadelphia: American Mathematical Society, 2015. — 234 p. This book is based on the program from 2011, Some Applications of Geometric Thinking. One goal of this course is to help teachers see that geometric ideas can be used throughout the secondary school curriculum, both as a hub that connects ideas from all parts of secondary school and beyond—algebra, number theory,...
Boca Raton: CRC Press, 2024. — 396 p. Preface The index of an isometric embedding Maximal ot-subsets of the Euclidean plane The cardinalities of at-sets in a real Hilbert space Isosceles triangles and it-sets in Euclidean space Some geometric consequences of Ramsey’s combinatorial theorem Convexly independent subsets of infinite sets of points Homogeneous coverings of the...
Springer, 2013. — 86 p. The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space....
American Mathematical Society, 2021. — 284 p. — (Pure and Applied Undergraduate Texts 51). — ISBN 9781470463076. Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs...
Springer, 2013. - 147 p. - Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized...
London: Imperial College Press, 2012. — 206 p. — ISBN: 1848168586. This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new...
Boca Raton: CRC Press, 2020. — 347 p. Finite Geometriesstands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on...
Springer, 2019. — 166 p. — ISBN: 9811339864. This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the...
Toronto: University of Toronto Press, 1969. — 383 p. This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods,...
Springer, 2015. — 761 p.
This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography.
The encyclopedia is of particular interest to...
Basel: Birkhäuser, 2012. — 286 p. This book is an outgrowth of the special term "Harmonic Analysis, Representation Theory, and Integral Geometry," held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007. The contributions in the volume provide a window into a variety of subjects related to reductive...
ArclerPress, 2024. — 315 p. Geometry Fundamentals is a crucial branch of mathematics that explores the relationships and properties of shapes, sizes, and spatial configurations in our world. From the simple lines and angles of two-dimensional figures to the complex three-dimensional structures, geometry provides a profound understanding of the fundamental principles governing...
Arcler Press, 2024. — 254 p. Computational Geometry is a branch of mathematics that deals with the solution of geometric problems that emerge in a variety of applications such as geographic information systems, robotics, and computer graphics, among others. Computational Geometry is covered in-depth in this Handbook, which provides an overview of key concepts and results in the...
Kolkata: Techno World, 2014.— 314 p. This book is an introduction to the concepts, major results and techniques in quintessential Riemannian Geometry. All the concepts are geometrically motivated. Concepts are explained with a set of important examples. The discerning reader will find some unusual examples that are usually hard to find in a book of this nature. Variety of...
Hindustan Book Agency (India), 2005. — 242 p. — (Texts and Readings in Mathematics 30) — ISBN: 978-81-85931-50-0. This book is written as an attempt to entice the students of mathematics to the world of geometry. In spite of the great strides made in modern geometry at research level, there is no introductory book which gives modern aspects of geometry at undergraduate/graduate...
Moscow: Mir Publishers, 1978. — 211 p. The book contains a collection of 1351 problems (with answers) in plane and solid geometry for technical schools and colleges. The problems are of varied content, involving calculations, proof, construction of diagrams, and determination of the spatial location of geometrical points. It gives sufficient problems to meet the needs of...
Athens: Nikos D. Kyriazis, 2018. — 409 p. History Harmonic Geometry is a New Geometry, pioneering, innovative and novel, which emerged after many years of rese 2018.arch. Thus, in addition to our well-known Geometries: Descriptive, Analytic, Projective, Differential, etc., we now also have Harmonic Geometry. Definition Harmonic Geometry is that field of Euclidean Geometry that...
European Mathematical Society, 2015. — 197 p. — (EMS Textbooks in Mathematics) — ISBN: 3037191511 Spectral theory is a diverse area of mathematics that derives its motivations, goals, and impetus from several sources. In particular, the spectral theory of the Laplacian on a compact Riemannian manifold is a central object in differential geometry. From a physical point a view,...
Routledge, 1989. - 288 pages.
The Ethics of Geometry is a study of the relationship between philosophy and mathematics. Essential differences in the ethos of mathematics, for example, the customary ways of undertaking and understanding mathematical procedures and their objects, provide insight into the fundamental issues in the quarrel of moderns with ancients. Two signal...
Springer, 2011. — xiv, 456 p. — ISBN 978-1-4614-1128-4, 978-1-4614-1129-1. The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the...
Computer Science at Narvik University College (NUC), 2012. — 325 p. Geometry – from Ancient Greek, earth measurement – has been an important ingredient of the development of science and later also industry, design and production. In modern time, the Geometric modeling community is established, and has now a 50-year-old history. The first pioneers were motivated by the...
Cambridge: Cambridge University Press, 2017. — 351 p. — (Cambridge Studies in Advanced Mathematics 169). — ISBN: 978-1-107-19923-1. Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical...
Robert J. Lang, 2003. - 55 pages.
Origami is the art of folding uncut sheets of paper into interesting and beautiful shapes. Within this text, the author presents a variety of techniques for origami geometric constructions. The field is rich and varied, with surprising connections to other branches of mathematics.
Compass-and-straightedge geometric constructions are familiar...
Second edition. — Springer, 1988. — 408 p. — ISBN: 0-387-96654-4. At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. They also show students the fundamental concepts and...
CRC Press, 2019. — 306 p. Volume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the recent aspects of volume, introduces problems related to it, and presents...
Springer International Publishing, Switzerland, 2017. — 685 p. — (Springer Monographs in Mathematics) — ISBN: 3319447041. This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums....
Springer, 2006. - 472 pages. ISBN: 0387332855
Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to...
Basel: Birkhäuser, 2000. - 277 p. Complex Dimensions of Ordinary Fractal Strings Complex Dimensions of Self-Similar Fractal Strings Generalized Fractal Strings Viewed as Measures Explicit Formulas for Generalized Fractal Strings The Geometry and the Spectrum of Fractal Strings Tubular Neighborhoods and Minkowski Measurability The Riemann Hypothesis, Inverse Spectral Problems...
Basel: Birkhäuser, 2021. — 690 p. This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides...
Prentice Hall, 1995. — 282 p. — ISBN: 0132908425
This book provides an accessible introduction to methods in computational geometry and computer graphics. It emphasizes the efficient object-oriented implemenation of geometric methods with useable C++ code for all methods discussed.
2nd Edition. — Springer, 2018. — 447 p. — (Graduate Texts in Mathematics 176). — ISBN: 978-3-319-91754-2. This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian...
University of Washington, 2000 - 474 c.
Учебник представляет собой вводный курс теории гладких многообразий для студентов, которые уже знакомы с общей топологией, линейной алгеброй и основами математического анализа.
Springer, 1997. - 224 c.
Учебник для студентов, в котором автор в простой, доступной форме знакомит читателей с основами римановой геометрии, особое внимание уделяя понятиям связности, геодезических и кривизны.
American Mathematical Society, 2012. — 479 p. Euclid. Incidence Geometry. Axioms for Plane Geometry. Angles. Triangles. Models of Neutral Geometry. Perpendicular and Parallel Lines. Polygons. Quadrilaterals. The Euclidean Parallel Postulate. Area. Similarity. Right Triangles. Circles. Circumference and Circular Area. Compass and Straightedge Constructions. The Parallel...
New York: Springer, 2020. — 264 p. This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end,...
Hoboken: John Wiley & Sons, Inc., 2014. — 493 p. Preface Euclidean Geometry Congruency Introduction Congruent Figures Parallel Lines Angles in a Triangle Thales' Theorem Quadrilaterals More About Congruency Perpendiculars and Angle Bisectors Construction Problems The Method of Loci Solutions to Selected Exercises Problems Concurrency Perpendicular Bisectors Angle Bisectors...
Hoboken: Wiley, 2015. — 336 p. A gentle introduction to the geometry of convex sets in n-dimensional space. Geometry of Convex Sets begins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space. Many properties of convex sets can be discovered using just the linear...
Hoboken: Wiley, 2014. — 172 p.
Written by well-known mathematical problem solvers, Classical Geometry: Euclidean, Transformational, Inversive, and Projective features up-to-date and applicable coverage of the wide spectrum of geometry and aids readers in learning the art of logical reasoning, modeling, and proof. With its reader-friendly approach, this undergraduate text...
Wiley, 2014. — 494 p. — ISBN: 1118679199, 9781118679197 Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader–friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial...
Springer, 2010. — 174 p. — ISBN 978-1-84996-486-9. The groundbreaking documentary (accompanying this book), introduced by Arthur C. Clarke, has been shown in over 50 countries around the world. Twenty five years ago it brought the subject of fractals to the attention of the general public for the first time. The contributors to the film are joined in this comprehensive survey of...
Hong Kong University Press, 1995. - 356 pages. With the present volume the 3-book series on elementary mathematics is now complete. Like its two predecessors, Fundamental Concepts of Mathematics and Polynomials and Equations, the present book is addressed to a large leadership comprising Sixth Form students, first-year undergraduates and students of Institutes of Education. In...
Издательство Cambridge University Press, 1997, -186 pp. Mathematical Science Research Institute Publications - Volume 31 God is always doing geometry. What Plato meant by this is no clearer now than it was in the first century a.d., when the dinner conversation quoted above (which I'm about to paraphrase) took place. Diogenianus, one of the guests, recalls that it is Plato's...
Cambridge University Press, 2012. — 418 p. — (Cambridge Studies in Advanced Mathematics 134) — ISBN: 052137331X. The aim of this graduate-level text is to equip the reader with the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme is to present the interaction of partial differential equations and differential...
Springer, 2020. — 242 p. — (Springer Tracts in Mechanical Engineering). — ISBN: 9811387540. This book focuses on the synthesis of lower-mobility parallel manipulators, presenting a group-theory-based method that has the advantage of being geometrically intrinsic. Rotations and translations of a rigid body as well as a combination of the two can be expressed and handled...
Springer, 2017. — 317 p. This book offers a comprehensive introduction to Subdivision Surface Modeling Technology focusing not only on fundamental theories but also on practical applications. It furthers readers’ understanding of the contacts between spline surfaces and subdivision surfaces, enabling them to master the Subdivision Surface Modeling Technology for analyzing...
Basel: Birkhäuser, 2024. — 680 p. This undergraduate textbook provides a comprehensive treatment of Euclidean and transformational geometries, supplemented by substantial discussions of topics from various non-Euclidean and less commonly taught geometries, making it ideal for both mathematics majors and pre-service teachers. Emphasis is placed on developing students' deductive...
Jones and Bartlett Publishers, 2008. — 371 p. My goal with this text is to kindle in college geometry students a passion for problem solving and a love for mathematics. The book evolved out of my notes for a two-term sequence of courses in college geometry I have taught for many years. Because the sequence is required for prospective high school mathematics teachers, the...
Beograd: Naučno Delo, 1951. — 32 s. Nasao sam u geometriji izvesne nesavrenosti, koje drim za razlog toova nauka, ukoliko nije analiza, da sada nije mogla uiniti ni koraka naprediz onog stanja u kom nam ju je Euklid ostavio. U ta nesavrenstva raunamnejasnost prvih pojmova o geometriskim koliinama, nain na koji se zamiljamerenje njihovo, i naposletku vanu prazninu u teoriji...
Edited and translated by Athanase Papadopoulos. — European Mathematical Society Publishing House, 2010. — 323 p. — (Heritage of European Mathematics). — ISBN: 978-3-03719-087-6 Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the...
Cambridge: Cambridge University Press, 1961. — 209 p. This book opens up an important field of mathematics at an elementary level, one in which the element of aesthetic pleasure, both in the shapes of the curves and in their mathematical relationships, is dominant. This book describes methods of drawing plane curves, beginning with conic sections (parabola, ellipse and hyperbola),...
London: Clay C.J. and Sons, 1893. — 527 p. The following work will, I hope, be found to be a fairly complete elementary text-book on Plane Trigonometry, suitable for Schools and the Pass and Junior Honour classes of Universities. In the higher portion of the book I have endeavoured to present to the student, as simply as possible, the modern treatment of complex quantities, and...
Springer-Verlag, 2013. — 296 p. — (Springer Monographs in Mathematics). — ISBN: 3642396259. The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for...
Springer, 2013. — 238 p. — ISBN: 978-1-4614-7272-8. "Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean...
American Mathematical Society, 2019. — 458 p. — (Colloquium Publications 65). — ISBN: 9781470450878. Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that...
CRC Press, 2010. — 430 p. — ISBN13: 978-1-4398-6546-0. From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern...
Springer Nature Switzerland, 2024. — 342 p. Preface Inversion and Stereographic Projection Bend Formulas Graphs and Circle-Systems Spherical Geometry I Spherical Geometry II The Problem of Thirteen Balls Spherical Geometry III Geometric Probability on the Sphere Intersection Graphs of Spherical Caps Quartets on a Sphere Higher Dimensions The Cayley-Menger Determinant Casey's...
McGraw-Hill, 2017. - 383p. COORDINATE GEOMETRY BOOSTER with Problems & Solutions for JEE Main and Advanced is meant for aspirants preparing for the entrance examination of different technical institutions, especially NIT/IIT/BITSAT/IISc. In writing this book, I have drawn heavily from my long teaching experience at National Level Institutes. After many years of teaching, I have...
Sofia: Arhimed, 2015. — 239 p. The present book is devoted to students of the last school grades, university students, teachers, lecturers and all lovers of mathematics who want to enrich their knowledge and skills in complex numbers and their numerous applications in Euclidean Geometry . Few countries in the world include complex numbers in their secondary school curriculum...
W.H. Freeman and Company, 1982. — 470 pages. Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle - you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending...
Cham: Springer, 2022. — 386 p. This book collects selected contributions presented at the INdAM Workshop "Geometric Challenges in Isogeometric Analysis", held in Rome, Italy on January 27-31, 2020. It gives an overview of the forefront research on splines and their efficient use in isogeometric methods for the discretization of differential problems over complex and trimmed...
USA: Ginn & Company, Publ., 2005. — 85 p. — ISBN: 0486442624. This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. Its first two-thirds requires just a familiarity with plane and solid geometry and trigonometry, and calculus is employed only in the final part. It begins with the theorems common to Euclidean and...
Princeton University Press, 2014. — 208 pages. ISBN: 0691150990
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied...
Vieweg+Teubner Verlag, 2011. — 246 p. This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group...
Springer, 1982. — 525 p. — (Undergraduate Texts in Mathematics). — ISBN-13 978-0387906942. Основы геометрии и неевклидовой плоскости This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The...
Providence: American Mathematical Society, 2016. — 234 p. This volume contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held on November 27, 2014, in Besançon, France. The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense...
Springer, 2019. — 486 p. — ISBN: 978-3-030-03866-3. This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and...
American Mathematical Society, USA, 2001. — 296 p. — (Translations of Mathematical Monographs 202) — ISBN: 0821821091. The study of asymptotic solutions to nonlinear systems of partial differential equations is a very powerful tool in the analysis of such systems and their applications in physics, mechanics, and engineering. In the present book, the authors propose a new...
Springer, 2002. — 491 p. — (Graduate Texts in Mathematics 212). — ISBN: 978-0-387-95374-8. Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or...
Cambridge: Cambridge University Press, 2023. — 181 p. Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic...
Pergamon Press Ltd., 1962. — 176 p. The aim of this book is to give, in concise form, the whole of the geometry of the straight line, circle, plane and sphere, with their associated configurations such as triangle or cylinder, in so far as it is likely to be required for courses in mathematics in the United Kingdom for the G.C.E. at Advanced and Scholarship levels, or for...
Springer, 2017. — 160 p. — ISBN: 978-3-319-39375-9. This is the only book dedicated to the Geometry of Polycentric Ovals. It includes problem solving constructions and mathematical formulas. For anyone interested in drawing or recognizing an oval, this book gives all the necessary construction and calculation tools. More than 30 basic construction problems are solved, with...
Springer-Verlag New York 2011. — 2nd Ed. — (Interdisciplinary Applied Mathematics 11). — 448 pp. — ISBN: 978-1-4419-7891-2 (Print) 978-1-4419-7892-9 (Online). This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a workpiece, or end...
Zishka Publishing, 2019. — 206 p. — ISBN13: 978-1941691502. This workbook is designed to help students practice writing geometry proofs. The early chapters review terminology, notation, and the underlying principles. Another chapter outlines the strategy and offers tips. Nine fully-solved examples are provided to help serve as a guide. Each of the exercises is fully solved in...
Cambridge University Press, 2020. — 617 p. — (Encyclopedia of Mathematics and its Applications, 172). — ISBN: 978-1-108-48958-4. Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have...
Cambridge University Press, 2002. — 567 p. Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and...
Springer International Publishing, Switzerland, 2017. — 194 p. — (Compact Textbooks in Mathematics) — ISBN: 9783319428628 This book has been ten odd years in the making. The text evolved into a little booklet for the Dutch Zebra series (Epsilon publishers). This is a series of 60-page booklets aimed at high school pupils preparing for their final exams. As the old saying goes,...
3rd Edition. — CRC Press, 2022. — 473 p. — (Textbooks in Mathematics). — ISBN 0367187981, 9780367187989. This unique textbook combines traditional geometry with a contemporary approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, introduces axiomatic, Euclidean and non-Euclidean, and transformational geometry. The text...
Tübingen: Universität Tübingen, 2018. — 261 p. Tropical hypersurfaces in Rn. Projective space and other tropical toric varieties. Tropical cycles in Rn. Projective tropical geometry. Tropical cycles and the Chow group. Tropical manifolds. Tropical curves. Tropical jacobians.
BookSurge Publishing, 2006. — 246 p. This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in advanced undergraduate or first-year graduate courses. Plane Curves. Basic Theory of Elliptic Curves. Elliptic Curves...
Springer International Publishing, Switzerland, 2016. — 216 p. — ISBN10: 3319450255 This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data...
American Mathematical Society, 1995. — 390 p. In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way,...
Harwood Academic Publ, 2008. — 134 p. — (Reviews in Mathematics and Mathematical Physics, Volume 11, Part 2). — ISBN10: 190486872X. This survey paper is devoted to Hamiltonian geometry of integrable partial differential equations and the theory of infinite-dimensional symplectic and Poisson structures. Infinite-dimensional symplectic and Poisson geometry is closely connected...
Jones and Bartlett Publ., England, 1993. — 121 p. — ISBN: 0-86720-242-4. The complicated formulations of Riemannian geometry present a daunting aspect to the student This little book focuses on the central concept-curvature It gives a naive treatment of Riemannian geometry, based on surfaces in Rn rather than on abstract Riemannian manifolds. The more ophIstIcated mtnnslC...
2nd Edition. — Jones and Bartlett Publ., 1998. — 158 p. — ISBN10: 1568814712. This classic text serves as a tool for self-study; it is also used as a basic text for undergraduate courses in differential geometry. The author's ability to extract the essential elements of the theory in a lucid and concise fashion allows the student easy access to the material and enables the...
College Publications, London, UK, 2010. — 174 p. — (Studies in Logic. Volume 27) — ISBN10: 1848900228 The Theory of Inconsistency has a long lineage, stretching back to Herakleitos, Hegel and Marx. In the late twentieth-century, it was placed on a rigorous footing with the discovery of paraconsistent logic and inconsistent mathematics. Paraconsistent logics, many of which are...
University of Maryland, 2002, -122 pp. Курс лекций. Fixed-Radius Near Neighbors and Geometric Basics Orientations and Convex Hulls More Convex Hull Algorithms Line Segment Intersection Planar Graphs, Polygons and Art Galleries Polygon Triangulation Halfplane Intersection Linear Programming More Linear Programming and Smallest Enclosing Disk Orthogonal Range Searching and...
College Park, MD: University of Maryland, 2023. — 187 p. This is an introductory course on computational geometry and its applications. We will discuss techniques needed in designing and analyzing efficient algorithms and data structures for computational problems in discrete geometry, such as convex hulls, geometric intersections, geometric structures such as Voronoi diagrams...
4th Edition. — McGraw-Hill, 2008. — 216 p. — ISBN: 0071543503. Содержит 618 задач с решениями. Get a firm grasp of trigonometry with this simple-to-use guide! It can help you pump up your problem-solving skills, ace your exams, and reduce the time you need to spend studying. This thorough review of standard college courses in trigonometry has been updated to reflect the latest...
Sixth Edition. — McGraw-Hill Education, 2018. — 214 p. — ISBN: 978-1-26-001149-4. Tough Test Questions? Missed Lectures? Not Enough Time? Textbook too pricey? Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed...
Third edition. — Fort Valley State University, 1998. — 212 p. The book is complete in itself and can be used equally well by those who are studying trigonometry for the first time and those who are reviewing the fundamental principles and procedures of trigonometry. Each chapter contains a summary of the necessary definitions and theorems followed by a solved set of problems....
Prentice-Hall, 1994. — 461 p. — ISBN: 0-13-336363-5. This introduction to computational geometry is designed for beginners. It emphasizes simple randomized methods, developing basic principles with the help of planar applications, beginning with deterministic algorithms and shifting to randomized algorithms as the problems become more complex. It also explores higher...
Wiley India, 2013. — 490 p. — ISBN: 9788126535835. A reliable resource, mathematics for jee (main and advanced), geometry - vol.4 has proved to be useful for jee aspirants. This book was written by an expert author. It is written from the students point of view and is specially designed and based upon the jee examination pattern. This book examines all the concepts of geometry...
Aberdeen Proving Ground, Maryland: Army Research Laboratory (ARL), Advanced Computational and Information Sciences Directorate, 2001. — 12 p. Euclidean geometry is not practical for describing complex natural shapes. A real-time solution using a fractal geometry approach is presented. First, existing digital terrain elevation data (DTED) is analyzed, and then it is interpolated...
Springer, 2020. — 254 p. — (CRM Short Courses). — ISBN: 978-3-030-49863-4. This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is...
Springer, 2019. — 395 p. — (Signals and Communication Technology). — ISBN: 3030025195. This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different...
Springer, 2014. — 397 p. The first conference of the Geometric Sciences of Information (GSI, website at http://www.gsi2013.org/ includes slides and photos) took place downtown Paris (France), in August 2013. The call for papers received an enthusiastic worldwide response, resulting in about a 100 accepted submissions of an average length of eight pages, and organized into the...
Springer, 2021. — 282 p. — (Signals and Communication Technology). — ISBN 978-3-030-65458-0. This book focuses on information-geometric manifolds of structured data andmodels and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on...
New York: Morgan & Claypool, 2013. — 170 p. Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost...
Morgan & Claypool, 2022. — 129 p. — (Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography, and Imaging #34). — ISBN-13 9781636393278. Трассировка лучей на GPU в неевклидовых пространствах This book explores the visualization of three-dimensional non-Euclidean spaces using raytracing techniques in Graphics Processing Unit (GPU). This is...
European Mathematical Society, 2012. — 203 p. — (EMS Textbooks in Mathematics) — ISBN: 3037191120 Large scale geometry is the study of geometric objects viewed from a great distance. The idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of varc, Milnor, and Wolf on growth of groups. In the last decades, large scale geometry has found...
Berlin: Springer, 2020. — 608 p. — ISBN: 978-3-662-61052-7, 978-3-662-61053-4. This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective,...
Cham: Springer, 2021. — 724 p. This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian...
6., korrigierte und erweiterte Auflage. — Springer, 2018. — 299 S. Die Relativitätstheorie ist in ihren Kernaussagen nicht mehr umstritten, gilt aber noch immer als kompliziert und nur schwer verstehbar. Das liegt unter anderem an dem aufwendigen mathematischen Apparat, der schon zur Formulierung ihrer Ergebnisse und erst recht zum Nachvollziehen der Argumentation notwendig...
Cham: Springer, 2024. — 729 p. — (Progress in Mathematics, 354). — ISBN 978-3-031-58119-9. An LCK (locally conformally Kahler) manifold is a complex manifold admitting a Kahler covering with monodromy acting by homotheties. Hopf manifolds and their submanifolds are the prime examples. This book presents an introduction to the principles of LCK geometry (the first two parts) and...
New York: Dover Publications Inc., 1986. — 208 p. Parametric surfaces: local theory. Non-parametric surfaces. Surfaces that minimize area. Isothermal parameters. Bernstein's theorem. Parametric surfaces: global theory. Minimal surfaces with boundary. Parametric surfaces in E 3 . The Gauss map. Surfaces in E 3 . Gauss curvature and total curvature. Non-parametric surfaces in E 3...
ITexLi, 2024. — 192 p. — ISBN 1837696128 9781837696123 1837696136 9781837696130 1837696144 9781837696147. This book includes ten chapters that discuss applications and updates in fractal analysis across the full spectrum of sciences, including mathematical concepts, cities, material physics, medicine, climate, and image processing. It is a valuable source of knowledge for...
New York: Wiley, 1995. — 374 p. A complete, self-contained introduction to a powerful and resurging mathematical discipline . Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd?s. Nearly half the results presented in...
Natal (RN): Editora do IFRN, 2009. — 149 p. — ISBN 978-85-89571-53-1. Trabalhando com estudantes dos diversos cursos na área tecnológica e de ciências exatas, sempre procurei, com zelo de quem é perfeccionista. ser o mais claro e objetivo possível naquilo que me expunha a fazer como docente da disciplina de Geometria Analítica. Senti, durante anos a necessidade, por parte dos...
Los Angeles: UCLA, 2010. — 442 p. The subject of Discrete Geometry and Convex Polytopes has received much attention in recent decades, with an explosion of the work in the field. This book is an introduction , covering some familiar and popular topics as well as some old, forgotten, sometimes obscure, and at times very recent and exciting results. It is somewhat biased by my...
Springer Basel AG, 2004. — 164 p. — ISBN 9783034896290. Distributions and Fourier Transform Radon Transform The Funk Transform Reconstruction from Line Integrals Flat Integral Transform Incomplete Data Problems Spherical Transform and Inversion Algebraic Integral Transform Notes
Cham: Springer, 2024. — 608 p. This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been...
Cham: Springer, 2023. — 543 p. This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been...
European Mathematical Society, 2012. — 462 p. — (IRMA Lectures in Mathematics and Theoretical Physics 18). — ISBN: 978-3-03719-105-7. This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg, during two geometry master classes, in 2008 and 2009. The aim of the master classes was to give to fifth-year...
Cham: Springer, 2022. — 469 p. The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces),...
Cambridge: Cambridge University Press, 2023. — 369 p. This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the...
Brussels: Pons Editions, 2016. — 181 p. We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen according to authors’ aspiration and attraction, as a poet writes lyrics about spring according to his...
Springer, 1992. - 468 p. - Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating...
Springer, 1992. - 513 p. - Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating...
Springer, 1991. - 136 p. - This first volume of strategic activities is designed to develop through a hands-on approach, a basic mathematical understanding and appreciation of fractals. The concepts presented on fractals include self-similarity, the chaos game, and complexity as it relates to fractal dimension. These strategic activities have been developed from a sound...
Springer, 1992. - 194 p. - This second volume of strategic classroom activities is designed to develop, through a hands-on approach, a basic mathematical understanding and appreciation of fractals. The concepts presented on fractals include self-similarity, the chaos game, and complexity as it relates to fractal dimension. These strategic activities have been developed from a...
Springer, 2006. — 412 p. This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in...
CreateSpace, 2015. — 190 p. The Author: Anton Petrunin (Russia), professor at Penn. State University The book is meant to be rigorous, conservative, elementary and minimalistic. At the same time it includes about the maximum what students can absorb in one semester. Approximately third of the material used to be covered in high school, not any more. The present book is based on...
ArXiv.com, 2018. - 203 p. The Author: Anton Petrunin (Russia), professor at Penn. State University The book is meant to be rigorous, conservative, elementary and minimalistic. At the same time it includes about the maximum what students can absorb in one semester. Approximately third of the material used to be covered in high school, not any more. The present book is based on...
The Association for Mathematical Research, 2022. — 154 p. — ISBN: 9781959384014. The genre of this book is unusual: it is a collection of carefully selected problems in modern geometry , each having an elegant solution, usually based on a single non-trivial idea. The problems are supplied with sketches of solutions (called “semisolutions” ) and comprehensive references to the...
Cham: Springer Nature Switzerland, 2023. — 107 p. This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this...
ArXiv, 2017. — 140 p. Problems for the graduate students who want to improve their problem solving skills in geometry. This collection is about ideas, and it is not about theory. An idea might feel more comfortable in a suitable theory, but it has its own live and history and can speak for itself — I hope you will hear it. I am collecting these problems for fun, but they might...
Pennsylvania State University, 2018. — 178 p. These notes are based on lectures at MASS program (Mathematics Advanced Study Semesters at Pennsylvania State University) Fall semester 2018 . The course is designed for those who plan to do differential geometry in the future, or at least who want to have a solid ground to decide not to do it. The differential geometry of curves and...
World Scientific Publishing Co., 1995. — 450 p. — ISBN13: 978-9810214265. This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include...
Cambridge: Cambridge University Press, 1999. — 267 p. — (Cambridge Tracts in Mathematics 94). Now in paperback, this popular book gives a self-contained presentation of a number of recent results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas...
Moscow: Mir Publishers, 1987. — 317 p. This is a manual for the students of universities and teachers’ training colleges. Containing the compulsory course of geometry, its particular impact is on elementary topics. The book is, therefore, aimed at professional training of the school or university teacher-to-be. The first part, analytic geometry, is easy to assimilate, and actually...
Springer, 2010. — 257 p. — (Western Ontario series in philosophy of science 83). — ISBN 978-90-481-9415-5. Moritz Pasch (1843–1930) has a secure reputation as a key figur in the history of axiomatic geometry. Less well known are his contributions to other areas of founda tional research. This volume features English translations of fourteen papers Pasch published in the decade...
Cambridge University Press, 2001. — 513 p. — (Encyclopedia of Mathematics and Its Applications 84). — ISBN 0 521 66058 0. One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections...
Cham: Springer Nature Switzerland, 2022. — 292 p. This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by |x|p + |y|p = 1 where p ≥ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric...
2nd edition. — CRC Press, 2022. — 485 p. — ISBN 9780367680749. Praise for the previous edition [...] Dr. Popko’s elegant new book extends both the science and the art of spherical modeling to include Computer-Aided Design and applications, which I would never have imagined when I started down this fascinating and rewarding path. His lovely illustrations bring the subject to...
Cambridge University Press, 1981. — 500 pages. ISBN: 0521298393 The earlier chapter of this self-contained text provide a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place. In parallel with this is an account, also from first principles, of the elementary theory of topological...
Springer Science & Business Media, 2002. — 263 p. — ISBN: 1930190859. State curriculum standards are mandating more coverage of geometry, as are the curricula for pre–service mathematics education and in–service teaching. Yet many secondary teachers know just enough geometry to stay one chapter ahead of their students! What′s more, most college–level geometry texts don′t...
Prometheus Books, 2012. — 387 p. — ISBN: 1616145870. Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure...
Springer – 2010, 572 pages, with 264 figures.
ISBN: 9783540420583
The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geometrical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from...
Springer, 2022. — 278 p. — (Moscow Lectures 08). — ISBN-13 9783030922481. This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces. The chapter on the differential geometry of plane curves considers local and global...
Second Printing. — Springer-Verlag, 1988. — xiv, 398 p. — (Texts and monographs in computer science). — ISBN 0-387-96131-3; ISBN 3-540-96131-3. The second printing of this book offers an excellent opportunity to correct the (forgivable) typos and the (less forgivable) imprecisions or minor errors of the first edition. Moreover, in the three years intervening between the two...
American Mathematical Society, USA, 2013. — 298 p. — (Contemporary mathematics 598) — ISBN: 0821887386. This volume contains the proceedings of the AMS Special Session on Radon Transforms and Geometric Analysis, in honour of Sigurdur Helgason's 85th Birthday, held from January 4-7, 2012, in Boston, MA, and the Tufts University Workshop on Geometric Analysis on Euclidean and...
Cham: Springer Nature Switzerland, 2024. — 185 p. This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics. Organized into four chapters, this work serves as a stepping stone for readers to delve into the subject, providing a succinct and...
Birkhäuser Verlag AG, 2007. — 225 p. — ISBN: 9783764375171 This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich...
New York: Springer, 1995. - 289p. This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis...
New York: Springer, 2019. — 812 p. This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This third edition greatly expands upon the second with an abundance of additional content, including a section dedicated to arithmetic hyperbolic groups. Over 40 new lemmas, theorems, and corollaries...
Springer, 2012. — 473 p. — ISBN: 3540349243.
На англ. языке.
Cinderella.2 это программный пакет для использования в аналитической геометрии.
Cinderella.2, the new version of the well-known interactive geometry software , has become an even more versatile tool than its predecessor. It now consists of three connected parts: An enhanced geometry component with new features...
Cham: Springer, 2022. — 310 p. This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD coursesTechniques in enumerative geometry (2019)and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more...
New York: Benziger Inc, 1971. — 784 p. Geometry is one of a series of five mathematics textbooks for junior and senior high schools. It is designed for a one-year course for students with a background of informal geometry and elementary algebra such as that included in Mathematics I, Mathematics II, and Algebra of this series. In its formal development of Euclidean geometry,...
ETH Zurich, 2020. — 313 p. These are notes for the lecture course “Differential Geometry I” given by the second author at ETH Zurich in the fall semester 2017. They are based on a lecture course given by the first author at the University of Wisconsin–Madison in the fall semester 1983. One can distinguish extrinsic differential geometry and intrinsic differential geometry . The...
Zürich: ETH, 2017. — 310 p. These are notes for the lecture course “Differential Geometry I” given by the second author at ETH Zürich in the fall semester 2017. They are based on a lecture course given by the first author at the University of Wisconsin–Madison in the fall semester 1983. What is Differential Geometry? Foundations. The Levi-Civita Connection. Geodesics. Curvature....
Cambridge: Cambridge University Press, 1984. — 136 p. This book describes a fresh approach to the classification of of convex plane polygons and of convex polyhedra according to their symmetry properties, based on ideas of topology and transformation group theory. Although there is considerable agreement with traditional treatments, a number of new concepts emerge that present...
Cambridge: Cambridge University Press, 1971. — 182 p. This tract provides an introduction to four finite geometrical systems and to the theory of projective planes. Of the four geometries, one is based on a nine-element field and the other three can be constructed from the nine-element 'miniquaternion algebra', a simple system which has many though not all the properties of a...
Springer, 2014. — 243 p. — ISBN: 9783319046747 This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical...
New York: Dover Publications, 1977. — 164 p. This book is about the fourth dimension and the structure of our universe. My goal has been to present an intuitive picture of the curved space-time we call home. There are a number of excellent introductions to the separate topics treated here, but there has been no prior weaving of them into a sustained visual account. I looked for...
Springer, 2016. — 257 p. Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller...
Cambridge: Cambridge University Press, 1986. - 215p.
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle...
New York: Kluwer Academic Publishers. – 2004. – 330 p. As K. Nomizu has justly noted, Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. The detailed consideration of involutive sums of Lie algebras has shown, however, that their role is more...
Salzmann H., Betten D., Grundhöfer T., Hähl H., Löwen R., Stroppel M. Berlin: Walter de Gruyter, 2011. — 706 p. This is the book that everybody interested in topological (incidence) geometry has been waiting for. It is the most comprehensive account of all important results relating to compact projective planes and for years to come it will be the standard reference and a must...
Saarbrücken: LAP Lambert Academic Publishing, 2013. — 220 p. In contrast with quantum theory, classical field theory can be formulated in a strict mathematical way by treating classical fields and dynamic variables as sections of smooth fiber bundles. This book aims to compile the relevant material on fiber bundles, jet manifolds, connections, graded manifolds and Lagrangian...
John Wiley & Sons, 2003. - 320 pages.
Advances in Geometric Modeling illustrates the significance of Geometric Modeling in construction, design and manufacture, in not only the traditional industries such as automobile and aircraft manufacturing, but also in modern industry. This includes CAD/CAM, Computer Art, Entertainment, Education and Training, Visualization, robotics,...
Cham: Springer, 2022. — 352 p. This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn–Minkowski theory. Giving an introduction to convex cones, it describes their most important geometric functionals, such as conic intrinsic volumes and...
Princeton: Princeton University Press, 2020. — 260 p. — (Annals of Mathematics Studies, 207). — ISBN: 978-0-691-20209-9, 978-0-691-20208-2, 978-0-691-20215-0. Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new...
Basel: MDPI, 2018. — 326 p. Symmetry is an intriguing phenomenon manifesting itself in art, nature, and the mind. This Special Issue book features 19 articles about discrete geometric and combinatorial polyhedral structures, with symmetry as the unifying theme. These articles present an attractive mix of topics and have appeared in two related Special Issues of Symmetry, on...
Philadelphia: American Mathematical Society, 2011. — 330 p. This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much...
Philadelphia: American Mathematical Society, 2014. — 226 p. A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmuller theory....
Oxford: Oxford University Press, 2001. — 176 p. The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincaré inequalities, concerning the relationship between the...
Springer, 2008. — 272 p. Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and modern architectural designs, in number theoretic problems, in models of biological shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance...
Emeryville, USA: Key Curriculum Press, 2008. — 837 p. — ISBN: 1559538821. Discovering Geometry includes all of the teaching resources necessary to enrich learning and to make the teaching experience more rewarding. In addition to a comprehensive, wraparound-style Teacher's Edition, you'll receive a spectrum of evaluation and assessment tools that let all students demonstrate...
Springer, 2013. — 326 p. — 3rd ed. — ISBN: 3642379559, 9783642379550
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other...
Springer, 2013. — 262 p. — 3rd ed. — ISBN: 3642380093, 9783642380099
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other...
VSP, Utrecht, The Netherlands, 1994. Stimulated by internal demands of mathematics, in recent years integral geometry has gain a powerful impetus from computer tomography. Now integral geometry serves as the mathematical background for tomography which in turn provides most of the problems for the former. The book deals with integral geometry of symmetric tensor fields. This...
Pearson Education, 2021. — 765 p. — ISBN 9353946751. This is the first book of JEE Advanced Mathematics series. The book is enriched with detailed exhaustive theory that introduces the concepts of mathematics in a clear, concise, thorough and easy-to-understand language. A large collection of relevant problems is provided in eight major categories (including updated archive for...
Springer, 2023. — 241 p. — (Undergraduate Texts in Mathematics). — ISBN 303125001X. The principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals , such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear...
Boca Raton: CRC Press, 1995. — 560 p. The Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial)
European Mathematical Society, 2016. — 196 p. — (IRMA Lectures in Mathematics & Theoretical Physics 25). — ISBN-13 9783037191583. This book studies a new theory of metric geometry on metric measure spaces, originally developed by M. Gromov in his book “Metric Structures for Riemannian and Non-Riemannian Spaces” and based on the idea of the concentration of measure phenomenon...
Springer, 2010. - 676 pages.
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line...
Thomson, 1973. — 371 p. — ISBN: 0818500514, 9780818500510
This comprehensive, best-selling text focuses on the study of many different geometries - rather than a single geometry - and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced...
Издательство John Wiley, 2000, -507 pp. This book is a text for an upper-division general geometry course offered by many universities. It builds on knowledge gained in school and lower-division university courses, to introduce advanced geometry, emphasizing transformations and symmetry groups in two and three dimensions. These theories underly many fields of advanced...
Springer, 2000. — 173 p. — (Universitext). — ISBN: 0387989803. The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but...
Academic Press, 1971. — 435 p. Affine geometry Intuitive Affine Geometry Axioms for Affine Geometry A Concrete Model for Affine Space Translations Affine Subspaces Intersection of Affine Subspaces Coordinates for Affine Subspaces Analytic Geometry Parallelism Affine Subspaces Spanned by Points The Group of Dilations The Ratio of a Dilation Dilations in Terms of Coordinates The...
Birkhauser, 2013. — 373 p. The first book of its kind uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction,...
Springer, 2010. - 348 pages, ISBN: 978-0-387-75470-3 Originally published by Center of Excellence, 1991. This is a reprinting with updates to the material and corrections. Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s...
Springer, 2009. - 176 pages.
This delightful book considers and solves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant for clever high school students and college students interested in geometry, but even mature mathematicians will find...
World Scientific, 2015. — 415 p. This book provides a systematic treatment of algebraic and topological properties of convex sets (possibly nonclosed or unbounded) in the ndimensional Euclidean space. Topics under consideration include general properties of convex sets and convex hulls, cones and conic hulls, polyhedral sets, the extreme structure, support and separation...
Chicago: The Open Court Publishing Co., 1919. – 274 p. Historical Elementary Hyperbolic Geometry Elliptic Geometry Analytical Geometry Representations of Non-Euclidean Geometry in Euclidean Space "Space-Curvature" and the Philosophical Bearing of Non-Euclidean Geometry Radical Axes, Homothetic Centres, and Systems of Circles Inversion and Allied Transformations The Conic
Pergamon Press Ltd., 1963. — 143 p. This textbook contains a treatment of the various topics in analytical geometry which are required for the advanced and scholarship levels in mathematics of the various Examining Boards. The text begins with a chapter on coordinates, distance, ratio, area of a triangle and the concept of a locus. This is followed by chapters on the straight...
Basel: Birkhäuser, 2016. - 527p. Provides a complete and rigorous axiomatic treatment of Euclidean geometry Proofs for many theorems are worked out in detail Takes a modern approach by replacing congruence axioms with a transformational definition of congruence In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using...
Amsterdam: North Holland, 2021. — 250 p. — (Handbook of Statistics 45). The subject of information geometry blends several areas of statistics, computer science, physics, and mathematics. The subject evolved from the groundbreaking article published by legendary statistician C.R. Rao in 1945. His works led to the creation of Cramer-Rao bounds, Rao distance, and...
Sudbury: Jones and Bartlett Publishers, 2008. — 272 p. Stahl's Second Edition continues to provide students with the elementary and constructive development of modern geometry that brings them closer to current geometric research At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing the students' understanding of...
Springer, 1992. - 228p. - ISBN: 0-387-97743-0 The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is...
Springer, 2005. — 241 p. — (Undergraduate Texts in Mathematics). — ISBN: 0-387-25530-3, 978-0-387-25530-9. This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the...
New York: Chapman and Hall/CRC, 2016. — 262 p. The main topic is what the title indicates: to collect, survey and categorize the results and theories achieved in the last 30 years with “polynomial methods”, mostly (but not exclusively) in finite geometries. It contains techniques based on the careful examination of coefficients of polynomials, resultants, algebraic curves,...
Springer, 2012. — 240 pages. — ISBN: 1461402980
This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a...
2nd Edition. - Springer, 2021. — 263 p. — ISBN 978-3-030-51668-0. This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets,...
Berlin: Heldermann Verlag, 1992. — 239 p. The author starts with the introduction of vector spaces, sesquilinear forms, and then studies the classical groups - special linear, symplectic, unitary and orthogonal groups - along the lines of E. Artin. Emphasis is placed on the "building" of the groups and their corresponding BN-pairs. Symplectic groups, unitary groups, orthogonal...
3rd Edition. — Cengage India, 2020. — 273 p. — ISBN 9353503795. Mathematics for Joint Entrance Examination JEE (Advanced): Coordinate Geometry (3E), a Cengage exam Crack series product, is designed to help aspiring engineers focus on the subject of Mathematics from two standpoints: to develop their caliber, aptitude, and attitude for the engineering field and profession. To...
4th ed. — McGraw-Hill, 2009. — 337 p. — ISBN: 978-0-07-154413-9. For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates its 50th birthday with a brand-new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest...
Mathematical Sciences Research Institute, 2002. — 379 pages.
The author's intent is to describe the very strong connection between geometry and lowdimensional topology in a way which will be useful and accessible (with some effort) to graduate students and mathematicians working in related fields, particularly 3-manifolds and Kleinian groups.
London: Pitman, 1947. — 153 p. A classical course of projective geometry. Linear Spaces and Coordinate Systems The Conic The Quadratic, Twisted Cubic and Linear Complex General Theory of Linear Collineations Linear Systems of Conic ans Quadratics Invariants and Covariants of Conics and Quadratics Miscellanious Examples
Springer, 2012. — 202 p. — (Springer Monographs in Mathematics). — ISBN: 3642256198. One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and...
Chapman & Hall/CRC, 2014. — 232 p. — (Textbooks in mathematics). —ISBN: 9781482234718, 1482234718. Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. The...
World Scientific Publishing, 2017. — 308 p. — ISBN: 978-981-3109-08-7. The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau's estimate of the first eigenvalue, the Lichnerowicz–Obata's theorem on...
Cambridge: Cambridge University Press, 2014. - 166p. This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function...
New York: Chapman and Hall/CRC, 2007. — 170 p. Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear...
Springer, 2004. — 241 p. — (Springer Series in Computational Mathematics 36). — ISBN: 3540211004. This book studies the original results, and their extensions, of the Russian mathematician S.A. Geršgorin who wrote a seminal paper in 1931 on how to easily obtain estimates of all n eigenvalues (characteristic values) of any given n-by-n complex matrix. The Gersgorin Circle...
2nd Edition. — Pearson Education, 2011. — 408 p. — ISBN 0-13-602058-5, 978-0-13-602058-5. Foundations of Geometry , Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the...
Springer, 2013. — 465 p. — ISBN: 9401039992. Integral geometry deals with the problem of determining functions by their integrals over given families of sets. These integrals define the corresponding integral transform and one of the main questions in integral geometry asks when this transform is injective. On the other hand, when we work with complex measures or forms,...
CRC Press, 1993, Pages: 388. CRC Standard Curves and Surfaces is a comprehensive illustrated catalog of curves and surfaces of geometric figures and algebraic, transcendental, and integral equations used in elementary and advanced mathematics. More than 800 graphics images are featured. Based on the successful CRC Handbook of Mathematical Curves and Surfaces, this new volume...
2nd Edition. — Taylor & Francis Group, 2006. — 556 p. — ISBN: 1584885998 Since the publication of the first edition, Mathematica has matured considerably and the computing power of desktop computers has increased greatly. This enables the presentation of more complex curves and surfaces as well as the efficient computation of formerly prohibitive graphical plots. Incorporating...
Springer International Publishing AG, 2017. — 199 p. — (Universitext) — ISBN: 978-3-319-65905-3. Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in...
2nd ed. — New York: Dover Publications, 2018. — 264 p. — (Dover Books on Mathematics). — ISBN 9780486816890. This book derives from author Nolan R. Wallach's notes for a course on symplectic geometry and Fourier analysis, which he delivered at Rutgers University in 1975 for an audience of graduate students in mathematics and their professors . The monograph is geared toward...
The Mathematical Association of America, 1996. - 108 p. - We are all familiar with the everyday notion of two-sided symmetry, as viewed for example in the external form of the human body. But in its broadest interpretation symmetry is a property which involves regularity and repetition. In this sense symmetry can be found everywhere, especially in science and art. The aim of this...
The Mathematical Association of America, 2001. - 133 Pages.
The Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. In this way, the Golden Section is no isolated phenomenon but rather, in many cases. the first and also the simplest...
Adelphi, Maryland: Army Research Laboratory (ARL), 1995. — 23 p. This study focused on developing a fractal dimension estimator which will be accurate over the limited range of fractal dimensions characteristic of the earth's natural relief. The estimator presented will have the advantage of reduced complexity and processing over the more optimal techniques. Local window...
Springer, 2017. — 320 p. — ISBN: 978-3-319-58183-5. Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal...
A K Peters/CRC Press, 2013. — 488 p. — ISBN 1466570970. Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic...
Cambridge University Press, 1974. — 228 p. — ISBN: 9780521098595. Models of the regular and semi-regular polyhedral solids have fascinated people for centuries. The Greeks knew the simplest of them. Since then the range of figures has grown; 75 are known today and are called, more generally, 'uniform' polyhedra. The author describes simply and carefully how to make models of...
McGraw-Hill, 2010. — 160 p. — ISBN: 0071638148. A no-nonsense practical guide to geometry, providing concise summaries, clear model examples, and plenty of practice, making this workbook the ideal complement to class study or self-study, preparation for exams or a brush-up on rusty skills. Established as a successful practical workbook series with more than 20 titles in the...
Boca Raton: CRC Press, 2019. — 347 p. — (Textbooks in Mathematics). — ISBN: 0367196905. Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to...
Sydney: Wild Egg Books, 2005. - 320 p. This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general...
New York, USA: The Dryden Press, 1945 (Reprint 2012). — 274 p. — ISBN: 0486498506. One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their...
Oxford University Press, USA, 2017. — 201 p. — ISBN: 0198784910. This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in an occasional series of volumes of CMI lectures. Although not explicitly linked, the topics in this inaugural...
Moscow: Mir Publishers, 1979. — 330 p. Why study non-Eucliean geometries?> The principal reason for the interest in hyperbolic geometry is the important fact of “non-uniqueness” of geometry; of the existence of many geometric systems. The non-uniqueness of geometry sheds new light on basic features of mathematics; on the role of idealization in science; on deductive knowledge...
New York: Academic Press, 1968. — 253 p. Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the...
Mathematical Association of America, 1987. — 246 p. This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in the NML series, but can be studied independently. It is devoted to the treatment of affine and projective transformations of the plane. These transformations include the congruencies and similarities investigated in the previous volumes. The simple...
Mathematical Association of America, 2009. — 285 p. Isaac M. Yaglom, an influential figure in mathematics and mathematics education in the Soviet Union during the 20th century, published his two volume Geometric Transformations in Russian in 1955 and 1956. The first volume was translated into English by Allen Shields and published as two separate texts in 1962 and 1968. The first...
Mathematical Association of America, 1961. — 144 p. The format of the book encourages active participation by the reader at all times. The first half contains the short, basic text and many problems, all interesting and mostly hard. The second half contains solutions in full as well as further comments. — Melvin Hausner, New York University Almost everyone is acquainted with plane...
Mathematical Association of America, 1984. — 202 p. This book is the sequel to Geometric Transformation I which appeared in this series in 1962. Part 1 treats length-preserving transformations (called isometries), this volume treats shape-preserving transformations (called similarities); and Part III treats affine and protective transformations. These classes of transformations...
Holden-Day Inc, 1968. — 300 p. — ISBN: 9780816299645, 0816299641. Designed for advanced undergraduate mathematics or physics courses, this volume focuses on "practical geometry, " emphasizing topics and techniques of maximal use in all areas of mathematics. Subjects include algebraic and combinatoric preliminaries, isometries and similarities, an introduction to crystallography,...
Edwards J.W., Ann Arbor, 1947. — 129 p. This volume proposes to supply to student and teacher a quick reference on properties of plane curves. Rather than a systematic or comprehensive study of curve theory, it is a collection of information which might be found useful in the classroom and in engineering practice. The alphabetical arrangement is given to aid in the search for...
Imo Training, 2007. -3 c.
I have taught classes at various math olympiad training programs. Here are some of my handouts and training material.
First three lemmas.
Theoretical base.
Excercises.
World Scientific Pub Co Inc, 2024. — 134 p. — ISBN-13: 978-981-128-333-8. This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear...
Springer, 2020. — 152 p. — (CRM Short Courses: Virtual Series on Symplectic Geometry). — ISBN: 978-3-030-37887-5. This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory. Functioning as a viable alternative to the standard algebraic analysis method, the categorical approach explored in this book makes microlocal sheaf theory...
New York: Nova Science Publishing, 2022. — 292 p. — (Mathematics Research Developments). — ISBN: 978-1-68507-885-0, 979-8-88697-064-7. This monograph briefly describes the properties of Euclidean geometry and Riemannian geometry. The significance of the genetic code in connection with the established laws of transmission of hereditary information in the polytope of hereditary...
New York: Spriger, 1996. — 166 p. Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an...
Cambridge: Cambridge University Press, 2006. — 186 p. Eight topics about the unit cubes are introduced within this textbook: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular Chuanming Zong demonstrates how deep analysis like log concave measure and the...
New York: Springer, 1999. — 256 p. Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject,...
Dover Publications, 1963. — 319 p. This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser...
Пер. с фр. — Москва, Ленинград: Государственное издательство технико-теоретической литературы, 1951. — 137 с. — (Геометрия Лобачевского и развитие ее идей. Выпуск 6). В книге известного французского математика Ж. Адамара показано фундаментальное значение метрики Лобачевского в теории автоморфных функций. От издательства Группа движений на плоскости Лобачевского и ее собственно...
Петропавловск: СКГУ им. М. Козыбаева, 2014. — 246 с. — ISBN: 978-601-272-777-7. В учебно-методическом пособии содержится курс лекций по дисциплине «Основания геометрии». В приложениях приведены разработки практических занятий, тестовые и семестровые задания, а также примерная тематика рефератов. Пособие предназначено для студентов вузов, обучающихся по специальности 5В010900...
М.: МЦНМО, 2007. — 136 с. Книга посвящена тем свойствам коник (кривых второго порядка), которые формулируются и доказываются на чисто геометрическом языке (проективном или метрическом). Эти свойства находят применение в разнообразных задачах, а их исследование интересно и поучительно. Изложение начинается с элементарных фактов и доведено до весьма нетривиальных результатов,...
М.: Московский центр непрерывного математического образования (МЦНМО), 2007. — 136 с. Книга посвящена тем свойствам коник (кривых второго порядка), которые формулируются и доказываются на чисто геометрическом языке (проективном или метрическом). Эти свойства находят применение в разнообразных задачах, а их исследование интересно и поучительно. Изложение начинается с...
М.-Л.: ОГИЗ, 1948. — 388 с. Данная книга посвящена изложению обширной и глубокой теории, которая была построена А.Д. Александровым начиная с 1940 г. Её предметом являются внутренние свойства выпуклой поверхности, т.е. такие свойства, которые могут быть обнаружены при помощи измерений, производимых на самой поверхности без обращения к объемлющему пространству. В теории А.Д....
Новосибирск: Наука, 2006. — lii + 748 с. — ISBN 5-02-032428-0. Академик А. Д. Александров (1912–1999) — один из крупнейших геометров XX в. В том 1 включены его статьи по теории смешанных объемов, геометрии «в целом», дифференциальным уравнениям эллиптического типа и основаниям теории относительности, оказавшие существенное влияние на развитие математики и вошедшие в золотой...
Новосибирск: Наука, 2007. — IV + 492 с.— ISBN 978-5-02-023184-9. Академик А. Д. Александров (1912–1999) — один из крупнейших геометров XX века. Том 2 представляет собой переиздание его знаменитой книги «Выпуклые многогранники», впервые опубликованной в 1950 г. и вошедшей в золотой фонд достижений отечественной науки. Настоящее издание содержит многочисленные комментарии и...
Новосибирск: Наука, 2008. — iv + 734 с. — ISBN 978-5-02-035566-8. Академик А. Д. Александров (1912–1999) — один из крупнейших геометров XX века. В том 3 включен перевод его выдающихся статей об аддитивных функциях множеств в абстрактных пространствах и об одном обобщении римановой геометрии, ранее не публиковавшихся на русском языке, его избранные статьи по философским и...
Учебное пособие для ВУЗов. — М.: Наука. Главная редакция физико-математической литературы, 1987. — 288 с. Содержит изложение оснований евклидовой геометрии, отправляющееся от простой, выводимой из практики системы аксиом геометрии на плоскости. За ним следуют выводы, создающие мост от аксиом к обычному изложению элементарной геометрии, включая учение о площади. Далее — аксиомы...
Учебное пособие. — М.: Наука, Главная редакция физико-математической литературы, 1990. — 672 с.: ил. — ISBN 5-02-014336-7. Содержит основные разделы курса геометрии: аналитическую геометрию, элементарную геометрию на основе аксиоматики, включая геометрические преобразования и построения, элементы многомерной и проективной геометрии, дифференциальной геометрии и топологии,...
Учебник. — 2-е издание, исправленное. — СПб.: БХВ-Петербург, 2010. — 624 с.: ил. — (Учебная литература для вузов).
Содержит основные разделы курса геометрии: аналитическую геометрию, элементарную геометрию на основе аксиоматики, включая геометрические преобразования и построения, элементы многомерной и проективной геометрии, дифференциальной геометрии и топологии, основания...
Пер с англ. Гусевский Н.А. — М.: Мир, 1986. — 112 с.: ил. — (Современная математика. Вводные курсы). Книга написана крупным американским специалистом по математическому анализу и содержит краткое и ясное изложение преобразования Мёбиуса в многомерном пространстве. Много внимания уделено применению современных методов топологии, эргодической теории, теории отображений и новым...
Учебное пособие. — М.: Наука, 1990. — 208 с. — ISBN 5-02-014288-3. Излагаются результаты по геометрии векторных полей в трехмерном евклидовом пространстве, начиная с работ Фосса, Синцова, Лилиенталя и др. Рассматриваются векторные поля в n-мерном пространстве, системы уравнений Пфаффа, внешние формы. Кратко излагаются некоторые топологические понятия, формулируется теорема де...
Учебник. — Изд. третье, исправленное. — Под ред. Э.3. Шуваловой. — М.: Наука, Главная редакция физико-математической литературы, 1966. — 228 c. Настоящий учебник составлен в соответствии с программой по математике для средних технических учебных заведений, утвержденной Министерством высшего и среднего специального образования СССР в 1964 г., и отражает внесенные в неё изменения.
Учебник. — Пермь: Пермский государственный гуманитарно-педагогический университет (ПГГПУ), 2015. — 172 с.: ил. — ISBN 2227-8397. Учебник «Многообразие геометрии» составлен в соответствии с требованиями федерального государственного образовательного стандарта высшего профессионального образования по направлению «Педагогическое образование». Учебник предназначен для изучения...
М.: МЦНМО, 2001. — 80 с. ISBN: 5-94057-012-7 Недавнее появление астроид и гипоциклоид в качестве ответов и моделей в целом ряде различных задач теории особенностей, теории каустик и волновых фронтов, теорий эволют и эвольвент, сделало ясным фундаментальное значение этих объектов и привело к открытию большого числа новых фактов, относящихся то к геометрии и анализу, то к физике...
Москва: «Просвещение», 1975. - 176 c. Настоящий задачник составлен в соответствии с новой программой по геометрии для студентов вторых курсов физико-математических факультетов педагогических институтов по специальности «математика». В нем отражена идея единства всех геометрических дисциплин. При составлении задачника имелось в виду, что, кроме студентов дневных отделений, им...
3-е изд. — М.: Лаборатория знаний, 2017. — 467 с. — ISBN 978-5-00101-453-9. Излагается геометрия Лобачевского на основе школьной аксиоматики абсолютной геометрии и аксиомы Лобачевского. Первая часть книги посвящена планиметрии Лобачевского, а вторая — стереометрии. В конце каждой главы даются задачи, в конце книги — ответы и указания к ним. Этим книга выгодно отличается от...
2-е изд., испр. — М. : БИНОМ, 2014. — 467 с. Излагается геометрия Лобачевского на основе школьной аксиоматики абсолютной геометрии и аксиомы Лобачевского. Первая часть книги посвящена планиметрии Лобачевского, а вторая — стереометрии. В конце каждой главы даются задачи, в конце книги — ответы и указания к ним. Этим книга выгодно отличается от других пособий по геометрии...
М.: Просвещение, 2001. — 336 с. — ISBN: 5090097348, 9785090097345. В учебном пособии излагается геометрия Лобачевского на основе школьной аксиоматики абсолютной геометрии и аксиомы Лобачевского. Первая часть книги посвящена планиметрии Лобачевского, а вторая часть - стереометрии. Книга может использоваться в классах с углубленным изучением математики, для индивидуальной работы...
Учеб. пособие для студентов физ.- мат. фак-тов пед. ин-тов. — М.: Просвещение, 1973. — 480 с.: ил. Учебное пособие для студентов физических и математических факультетов педагогических институтов. Дано изложение элементов векторной алгебры, геометрии на плоскости, теории прямой, теории плоскостей и квадрик в евклидовых и аффинных пространствах. Также излагаются такие вопросы...
Учеб. пособие для студентов физ.- мат. фак-тов пед. ин-тов. — М.: Просвещение, 1976. — 447 с.: ил. Книга является второй, заключительной частью учебного пособия по геометрии для студентов физико-математических факультетов педагогических институтов. В четырех разделах пособия излагаются такие вопросы программы, как проективная геометрия, теория построений на плоскости и методы...
М.: Просвещение, 1994. — 192 с: ил. — ISBN 5-09-004599-2. Задачник-практикум соответствует программе по геометрии для физико-математических факультетов педагогических институтов. Он содержит задачи по разделам: «Геометрические построения на плоскости», «Методы изображений и «Дифференциальная геометрия и топология». Задачник, ориентированный на учебные пособия 1 и 2, призван...
Москва: Просвещение, 1967. — 368 с.: ил. В книге изложены вопросы аксиоматики геометрии, афинная и проективная геометрия, элементы дифференциальной геометрии и необходимые сведения из топологии. Краткий и четкий язык изложения, достаточное число иллюстраций делают эту книгу полезным и доступным пособием для студентов как очных, так в заочных педагогических институтов....
Ханты-Мансийск: Полиграфист, 2008. - 280 с. ISBN/ISSN: 978-5-89846-794-4 В монографии излагаются недавние результаты работ авторов, а также других математиков, полученные в теории однородных римановых и псевдоримановых многообразий, теории однородных эйнштейновых многообразий, геометрии инвариантных структур на обобщенных симметрических пространствах, теории локально...
Улан-Удэ: Изд-во Бурятского госуниверситета, 2013. — 224 с. — ISBN: 978-5-9793-0549-3. Монография посвящена математической формулировке основ фрактальной геометрии и математического аппарата фрактального исчисления. Изложен канторовский метод измерения фрактальной размерности разветвленных структур. Вместе с традиционным материалом рассмотрены некоторые широко представленные в...
Учебное пособие для вузов. М.,"Высшая школа",1972.
В книге на основании систем аксиом Гильберта дается подробное обоснование многих понятий геометрии, изучаемых в средней школе. Материал некоторых параграфов выходит за рамки программы и может быть использован для спецкурсов, спецсеминаров по геометрии и курсовых работ.
М.: Наука, 1969. — 380 с.
Предлагаемая ныне вниманию русского читателя книга видного немецкого геометра, профессора университета в г. Киле и главы пользующейся почетной известностью кильской геометрической школы Фридриха Бахмана «Построение геометрии на основе понятия симметрии» представляет интерес в двух отношениях. Прежде всего это есть серьезное научное исследование,...
Перевод с немецкого А.И. Сирота. — М.: Мир, 1973. — 249 с. — (Современная математика. Популярная серия). В этой книге на вполне элементарном материале, начинающемся с простейших геометрических истин (середины сторон произвольного четырехугольника являются вершинами параллелограмма и т.д.), развита весьма изящная теория, устанавливающая зачастую совершенно неожиданные связи...
Владикавказ: ЮМИ ВНЦ РАН и РСО-А, 2012. — 414 с. — (Итоги науки. Юг России. Математическая монография. Вып. 4). В монографии излагаются как классические, так и недавно полученные результаты о векторных полях Киллинга и порождаемых ими однопараметрических группах изометрий римановых многообразий, а также о геодезических, являющихся интегральными кривыми киллинговых векторных...
Перевод с французского Ю. Н. Сударева, А. В. Пажитнова, С. В. Чмутова. Под редакцией И. Х. Сабитова. — М.: Мир, 1984. — 560 с.: ил. Книга известного французского математика охватывает широкий круг вопросов классической геометрии в современном изложении. В ней удачно сочетаются общие абстрактные идеи и многочисленные примеры конкретных приложений . Издание богато иллюстрировано....
Перевод с французского Ю. Н. Юдарева, В. В. Трофимова. Под редакцией И. Х. Сабитова. — М.: Мир, 1984. — 368 с.: ил. Книга известного французского математика охватывает широкий круг вопросов классической геометрии в современном изложении. В ней удачно сочетаются общие абстрактные идеи и многочисленные примеры конкретных приложений . Издание богато иллюстрировано. Во второй том...
М.: Мир, 1989. — 304 с. -ил. Сборник задач по геометрии. Составлен известным французским математиком М. Берже с соавторами, дополняющий двухтомный курс М. Берже "Геометрия" (М.: Мир, 1984). В начале каждой главы даны основные определения и теоремы, необходимые для решения задач. Приведены указания к решению, а в конце книги даны полные решения задач. Книга иллюстрирована...
СПб.: Университет ИТМО, 2017. — 56 с. Предлагаемое пособие предназначено для студентов первого курса академического бакалавриата. В первом разделе объясняется задание кривых в полярных координатах и параметрически. Во втором разделе приведены уравнения, основные геометрические свойства и иллюстрации большинства специальных кривых, встречающихся в математике и ее приложениях. В...
Пер. с нем. В.А. Залгаллера, С.И. Залгаллер. — М.: Наука, 1967. — 232 с.: ил. В книге прежде всего идет речь об изопериметрических свойствах круга (наименьшая длина кривой при заданной площади) и шара (наименьшая площадь при заданном объеме). Наряду с этим рассматриваются свойства выпуклых тел.
Москва-Ленинград, ОНТИ, 1934 г. - 226 с. Название "неевклидова геометрия" широкие круги читателей обычно связывают с именем Лобачевского; настоящая же работа посвящена другой неевклидовой геометрии, носящей имя немецкого математика Римана (точнее говоря, здесь главным образом будет идти речь об эллиптической форме ее). К обоснованию геометрии можно подходить различными путями:...
Пособие для учителей средней школы. — М.; Л.: Учпедгиз, 1949. — 321 с. Книга проф. С.А. Богомолова «Геометрия» (систематический курс) значительно отличается от других книг того же названия. Наиболее важные особенности этого курса следующие: Особенности этого курса: - полностью весь курс изложен на основе аксиоматического метода; - выдержан принцип фузионизма, позволивший автору...
Москва - Ленинград: Государственное учебно-педагогическое издательство Министерства просвещения РСФСР, 1949. - 321 с. Написано на базе лекций по основаниям геометрии, прочитанных автором в Ленинградском пединституте для студентов физико-математического факультета. Книга проф. С.А. Богомолова значительно отличается от других книг того же названия. Наиболее важные особенности...
Москва; Петроград: Госиздат, 1923. — 335 с. В основу настоящей книги легли лекции по "Основаниям Геометрии", которые автор читает уже в течение 15-ти лет в 1-ом Высшем Педагогическом Институте (бывш. Женский Пед. Инст.) За последние годы тот же курс автор излагал на Высших Н.-Пед. Курсах и в Педагогических Институтах имени Герцена и Некрасова. Перерабатывая названный курс в...
Ижевск: Регулярная и хаотическая динамика, 2001. — 128 с. Учебное пособие посвящено изложению основных идей фрактальной и мультифрактальной геометрии. Примеры различных фрактальных структур можно встретить во многих явлениях природы. Фрактальные образы с успехом используются при описании хаотического поведения нелинейных динамических и диссипативных систем, турбулентного...
М.: Наука. Физматлит, 1997. — 224 с. — ISBN: 5-02-015081-9. Посвящена современным проблемам геометрии. Рассмотрены вопросы, близкие к классической теореме Хелли и связанные со свойствами семейства транслятов (т.е. образов при параллельных переносах) выпуклых тел. Авторы дают полный обзор (с детальными доказательствами) результатов в этой области комбинаторной геометрии, начиная...
М.: Наука, 1965. — 108 с. — (Математическа библиотечка). В теории выпуклых фигур есть много изящных результатов, вполне доступных пониманию школьников и в то же время представляющих интерес для специалистов-математиков. Некоторые из таких результатов мы и хотим предложить вниманию читателя. Мы расскажем о комбинаторных задачах теории выпуклых фигур, связанных главным образом с...
Пер. с англ. К.И. Осколкова; Под ред. Б.С. Кашина. — М.: Мир, 1988. — 240 с.: ил. — ISBN 5-03-001115-3. Монография датского математика, отражающая результаты, полученные за последние годы в комбинаторной теории выпуклых многогранников. В ней представлены соотношения Дена-Соммервилля, теоремы Макмюллена и Барнетта о максимальном и минимальном числе граней. Изложение отличается...
М.; Л.: Государственное издательство технико-теоретической литературы (ГИТТЛ), 1951. — 127 с. — (Геометрия Лобачевского и развитие ее идей, Выпуск 4). Книга содержит оригинальное аналитическое изложение геометрии Лобачевского на плоскости. Геометрия Лобачевского развертывается главным образом в модели Пуанкаре, которую автор чрезвычайно удачно связывает с моделью...
Казань: Издательство Казанского университета, 1964. — 93 с. В настоящей работе дается изложение основных фактов конформной геометрии плоскости. Наряду с фактами аналитической геометрии (углы между кругами, пучки кругов и т. д. ) рассматриваются вопросы дифференциальной геометрии последовательности кругов, дифференциальной геометрии кривых на плоскости. В последнем параграфе...
Книга. — Киев: Типография Императорского Университета Св. Владимира, 1880. — XV, 747 с. Исследования геометров конца прошлого и настоящего столетий: Гаусса, Лежандра, Лобачевского, Болэя, Риммана, Бельтрами, Гельмгольца и других, относительно начал на которых воздвигнут геометрический строй нашего пространства, пролили яркий свет на эти начала, разорвать завесу, покрывавшую...
Учебное пособие. — СПб.: Российский государственный педагогический университет (РГПУ) имени А.И. Герцена, 2021. — 64 с. Это учебное пособие доступно каждому, кто изучал в школе стереометрию и интересуется геометрией. В нём рассматриваются невыпуклые однородные многогранники с выпуклыми гранями. Класс однородных многогранников содержит многогранники как с выпуклыми правильными...
Перевод с англ. Ю.Д. Бураго. — М: Наука, Главная редакция физико-математической литературы, 1982. — 480 с. Книга посвящена классификационным задачам теории пространств постоянной кривизны и симметрических пространств. Видное место в ней занимает принадлежащее автору полное решение классической проблемы сферических пространственных форм. Но охвачен значительно более широкий круг...
М.: МЦНМО, 2016. — 79 с. — (Библиотека Математическое просвещение. Выпуск 39). — ISBN: 978-5-4439-2472-4. Брошюра посвящена многомерному кубу и его свойствам. Рассказывается, как получить формулу для числа граней куба любой размерности и как распространить ее на другие правильные многогранники. Рассматриваются комбинаторные и топологические свойства многомерного куба, связанные...
ТЕТРУ Москва 2009 г. 268 стр.
Монография посвящена изложению основных идей, методов и физических приложений финслеровой геометрии. Показано, что физическому Миру соответствует не одна, а некоторый класс финслеровых геометрий. Предложенный принцип самодостаточности финслеровых геометрий позволил применить геометрический подход в теории поля, при этом гравитация и...
Перевод с седьмого немецкого издания И.С. Градштейна. — Под редакцией и вступительной статьёй П.К. Рашевского. — М.; Л.: ОГИЗ, Государственное издательство технико-теоретической литературы, 1948. — 491 с. — (Классики естествознания. Математика, механика, физика, астрономия). П. К. Рашевский. «Основания геометрии» Гильберта и их место в историческом развитии вопроса. Гильберт Д....
3-е изд. — М.: Наука, 1981. — 344 с. Книга представляет собой одно из лучших и исторически одно из первых популярных произведений по математике, написанных крупными математиками. В книге содержится, действительно, очень наглядный, но достаточно строгий рассказ о геометрических науках и теориях, в частности о геометрической кристаллографии, о геометрической сущности кинематики и...
Харьков: ОНТИ НКТП, 1934. — 53 с.
Книга проф. А. М. Гинзбурга „Симетрия на плоскости" представляет собою изложение теории симетрии на плоскости, в которую вошли многие изыскания самого автора. Автор, инженер по специальности и в то же время весьма солидный математик, в своих работах и исследованиях интересен именно тем, что связывает будто бы чисто математические вещи с...
2-е изд. (эл.) — М.: БИНОМ. Лаборатория знаний, 2012. — 247 с.
В 1937 году в двух номерах журнала «Математика в школе» была опубликована удивительная по содержанию и полноте изложения статья В. Б. Фурсенко под названием «Лексикографическое изложение конструктивных задач геометрии треугольника». Автор этой статьи на основе изучения многочисленной литературы на русском, немецком,...
4-е изд., испр. — М.: Лаборатория знаний, 2015. — 250 с. — ISBN: 978-5-9963-2510-8. Представлены все возможные построения треугольника по трем его элементам. Каждое построение предваряется анализом и условиями разрешимости. Приводятся решения задач, сформулированных в многочисленных пособиях по элементарной геометрии. Для учителей математики, учащихся 7–11 классов,...
Київ: Наукова думка, 2008. – 232 с.
Основні положення фрактальної геометрії.
Автомодельність та фрактали.
Детерміновані фрактали.
Розмірність та міра.
Самоафінні фрактали.
Мультифрактали.
Застосування фракталів у математиці, фізиці і астрофізиці.
Дробовий інтеграл і дробова похідна.
Термодинаміка і газодинаміка.
Електродинаміка.
Методи ренормування груп, кластеризації...
М.: ВШЭ, 2017. — 294 с. Это интенсивный годовой курс геометрии для студентов-математиков. Все встречающиеся в тексте упражнения существенны для его понимания и обычно используются в дальнейшем. К некоторым из них есть комментарии в конце книги. Неформальное введение Аффинная плоскость Аффинная группа Евклидова плоскость = комплексная прямая Многомерие Объёмы и определители...
Учебное пособие. — Хабаровск: Дальневосточный государственный университет путей сообщения (ДВГУПС), 2014. — 150 с. Учебное пособие соответствует ФГОС ВО по направлениям подготовки бакалавров 09.03.01 «Информатика и вычислительная техника» и 09.03.03 «Прикладная информатика». Рассмотрено, на основе изучения аналитической, аффинной и проективной геометрий, матричное представление...
2-е изд. стереотип. — Хабаровск: Дальневосточный государственный университет путей сообщения (ДВГУПС), 2013. — 135 с. Учебное пособие соответствует ФГОС ВПО по направлению подготовки бакалавров 230100.62 "Информатика и вычислительная техника" по профилю "Системы автоматизированного проектирования". Рассмотрены основные положения аффинной и проективной геометрии, описаны...
Учебное пособие. – Витебск : Витебский государственный университет имени П.М. Машерова, 2024. – 111 с. — ISBN 978-985-30-0153-2. Настоящее учебное пособие предназначено прежде всего для студен-тов, получающих общее высшее образование по специальности 6-05-0113-04 Физико-математическое образование и изучающих учебную дисциплину «Геометрические построения фигур и преобразования...
Пер. с англ. С.И. Залгаллер. — М.: Наука, 1971. — 96 с. — (Математическая библиотечка). Научно-популярная книга, рассчитанная на уровень младших курсов университетов, рассказывает о двух проблемах теории выпуклых тел. Первый очерк посвящён оценке степени симметричности выпуклых тел, второй "проблеме Борсука", разбиении выпуклых тел на возможно меньшее число частей, диаметр...
Учебное пособие. — Омск: Омский государственный педагогический университет (ОмГПУ), 2010. — 29 с.: ил. 34. — ISBN 978-5-8268-1440-6. В работе рассмотрен один из интереснейших вопросов курса геометрии – вопрос о равновеликости и равносоставленности геометрических фигур, который был поднят в конце XIX в. великим математиком Д. Гильбертом (он был сформулирован им в виде третьей...
Ръководство /учебно пособие/-второ преработено издание, издателство: Университет по архитектура строителство и геодезия /УАСГ/- София, България, 2009 г., 58 стр.
На български език.
Ръководството е предназначено за студентите от специалност Архитектура на УАСГ и се състои от 6 глави:
1. Монжова проекция
2. Аксонометрия
3. Равнинни сечения
4. Сенки на фигури върху повърхнини...
Навч. посібник. - Харків: ХНАМГ, 2011. −92 с. Теоретичний матеріал подається у досить стислій формі – наводяться основні означення і факти з концентрацією уваги на розкритті суті понять, їх взаємозв’язків без надмірної строгості викладу. Для кращого розуміння використовуються відповідні графічні ілюстрації. Закріпленню знань сприяють детально розібрані типові приклади. Для...
Учебное пособие. — Томск: Томский государственный педагогический университет (ТГПУ), 2009. — 72 с. — ISBN: 978-5-89428-408-8. В данном учебном пособии изложен минимум необходимых сведений из аналитической геометрии и линейной алгебры для изучения курса «Элементы вычислительной геометрии», даны основные понятия и приведено описание некоторых важных алгоритмов вычислительной...
Киев: Изд-во ИМ НАН Украины, 2010. — 124 с. (Працi Iнституту математики НАН України. Математика та її застосування. — 2010. — Т. 81. — 124 с.) Монографiя присвячена новим результатам в теорiї векторних розшарувань, насамперед, застосуванню технiки матричних задач до дослiдження й опису векторних розшарувань над особливими кривими. Розглянуто бiмодульнi категорiї, якi є основним...
2-е изд. переработанное. — М.: Наука, 1986. — 760 с. Книга включает геометрию Евклида и Минковского, их группы преобразований, классическую геометрию кривых и поверхностей, тензорный анализ и риманову геометрию, вариационное исчисление и теорию поля, основы теории относительности, понятие многообразия и важнейшие примеры, основы теории расслоений, гомотопий и гомологий,...
М.: Наука. Главная редакция физико-математической литературы, 1979. — 760 с. Книга включает геометрию пространств Евклида и Минковского, их группы преобразований, классическую геометрию кривых и поверхностей, тензорный анализ и риманову геометрию, вариационное исчисление и теорию поля, основы теории относительности, геометрию и топологию многообразий, в том числе основы теории...
4-е изд., исп. и доп. — М.: Эдиториал УРСС, 1998. — 336 с. — ISBN: 978-5-901006-02-Х. Книга включает геометрию пространства Евклида и Минковского, их группы преобразований, классическую геометрию кривых и поверхностей, тензорный анализ и риманову геометрию, вариационное исчисление и теорию поля, основы теории относительности. Книга рассчитана на студентов-математиков,...
4-е изд., исп. и доп. — М.: Эдиториал УРСС, 1998. — 280 с. — ISBN: 978-5-901006-27-5. Книга включает геометрию и топологию многообразий, в том числе основы теории гомотопии и расслоений, некоторые их приложения, в частности, к теории калибровочных полей. Книга рассчитана на студентов старших курсов, аспирантов и научных работников — математиков, механиков и физиков-теоретиков.
2-е изд., исп. — М.: Эдиториал УРСС, Добросвет, 2001. — 288 с. — ISBN: 978-5-8360-0162-6. Книга содержит доступное изложение методов теории гомологии, освобожденное от утомительного языка абстрактной гомологической алгебры. Более сложная часть книги содержит введение в современные методы вычисления гомотопических групп и классификации многообразий. Для научных работников...
Учебное пособие. — Пенза: Приволжское книжное издательство, 1972. — 172 с. Учебное пособие для учителей математики средней школы в качестве учебного пособия по факультативному курсу "Понятие о неевклидовых геометриях и об аксиоматическом методе в геометрии".
Учебное пособие. — М.: Просвещение, 1979. — 256 с. Первый раздел книги посвящен расширению и углублению вопросов школьного курса геометрии и объединенного курса геометрии I-II физ.-мат. факультетов пединститутов. Второй раздел посвящен дальнейшему развитию теории обобщенных пространств, имеющих важные приложения в теории относительности. В добавлении кратко рассматриваются...
6-е изд. — М.: Наука, 1978. — 576 с.: ил. Перед вами прекрасная книга, в которой с редкой ясностью и яркостью излагаются основы геометрии — евклидовой и неевклидовой, проективной геометрии, геометрии постоянной кривизны. Эта книга — классический учебник, выдержавший семь изданий, отличается методически продуманным и умело распределенным материалом и остается современной и...
7-е изд. — М.: Физматлит, 2004. — 584 с. — ISBN: 5-9221-0267-2. Перед вами прекрасная книга, в которой с редкой ясностью и яркостью излагаются основы геометрии — евклидовой и неевклидовой, проективной геометрии, геометрии постоянной кривизны. Эта книга — классический учебник, выдержавший семь изданий, отличается методически продуманным и умело распределенным материалом и...
5-е издание. — М.: Наука, 1971. — 576 с. В настоящее (пятое) издание внесены небольшие изменения в отдельных местах книги, где требовались поправки и некоторые улучшения прежнего текста. Основания геометрии. Проективная геометрия. Геометрия постоянной кривизны.
М.: Фима , 2007. — 112 с. — ISBN 5-89492-015-9 Посвящена качественной геометрии, главным образом задачам классификации пространств с точностью до равномерно непрерывных изображений. Особое внимание уделено плоскости и пространству Лобачевского и качественным отличиям этих пространств от евклидовых. Первые главы книги не предполагают специальной подготовки и пригодны для...
Л.; М.: ОНТИ, НКТП, Главная редакция технико-теоретической литературы, 1937. — 296 с. Книга представляет собой систематический сборник задач по основным разделам дифференциальной геометрию.
Учебное пособие. — Ярославль: Ярославский государственный педагогический университет (ЯГПУ) имени К.Д. Ушинского, 2013. — 78 с. Данная работа предназначена для студентов дневного и заочного отделений педагогических вузов, специализирующихся в области информатики. Работа составлена на основе опыта преподавания данного курса на физико-математическом факультете ЯГПУ для студентов...
Москва: МЦНМО, 2004. — 86 с. В книге изложены элементы теории геометрических преобразований. Рассмотрены движения плоскости, преобразования подобия, аффинные, круговые и проективные преобразования. Описано построение моделей геометрии Лобачевского с помощью проективных и круговых преобразований. Пособие написано на основе спецкурса, который вел автор в гимназии № 1543. Оно...
Однородные координаты - мощный инструмент, находящий своё применение в различных разделах компьютерной графики - геометрическом моделировании, визуализации, машинном зрении и т.д. Однородные координаты явно или неявно используются в любом графическом пакете на этапах преобразования и затенения геометрии. Например в OpenGL или DirectX. В данной статье даётся определение и некоторые...
Саратов: Научная книга, 2004. — 84 с. Раздел "Основания геометрии" завершает курс геометрии, изучаемый студентами математических специальностей университетов и педагогических вузов. В нём геометрия рассматривается с позиций её аксиоматического построения. В настоящем пособии имеется параграф, освещающий основные этапы развития учения об обосновании геометрии. В качестве...
М.; Л.: Государственное издательство, 1930. — 67 с. В книге дано такое изложение первых понятий и теорем геометрии и тригонометрии Лобачевского, которое не строже изложения учебников Давидова и Киселева и не труднее его. Приводятся только те понятия и теоремы геометрии Лобачевского, которые необходимы для вывода основных формул его тригонометрии. Предисловие редактора....
LAP LAMBERT Academic Publishing, 2013. — 92 с. В данном исследовании мы рассмотрим этапы открытия явления фрактальности, представим основные понятия и методологические подходы, которые применяются в настоящей работе. Будет проведен обзор имеющихся исследований (включая авторские) по фрактальности в различных сферах – в лингвистике, математике и, что особенно важно для нашей...
Одесса: Mathesis, 1913. — 27 с. Доклад, прочитанный в Общем Собрании Первого Всероссийского Съезда преподавателей математики. Рассказано о различных методиках геометрических расчетов и преобразований. Постановка задачи. Несколько слов об однородных уравнениях. О скелете разложения. Об отрезках разложения. Дополнительно приложен видеоматериал о многогранниках, длительность...
М.; Л.: Государственное издательство технико-технической литературы, 1949. — 492 с. Первая часть, составляющая содержание настоящего тома, посвящена обстоятельному изложению геометрии Лобачевского, этого основного творения, на котором прежде всего построено современное учение об основаниях геометрии, если не об обосновании всей вообще математики. Совершенно естественно...
М.; Л.: Государственное издательство технико-теоретической литературы, 1956. — 344 с. Во вторую часть предполагалось включить историю признания геометрии Лобачевского и доказательство ее непротиворечивости на базе изучения важнейших ее интерпретаций. Наконец, третья часть должна была содержать аксиоматику евклидовой и неевклидовых геометрий вместе с построением их на...
М.: Издательство Московского университета, 1960. — 207 с. По лекциям Эли Картана, читанным в Сорбонне в 1926-1927 гг. Перевод с французского и редакция проф. С. П. Финикова. Имея в виду, что студенты Сорбонны по каждому предмету, который они выбирают, сдают и письменный, и устный экзамены, а письменный экзамен представляет собой решение задачи, предложенной на тему прочитанного...
Пер. с англ. А.В. Овчинников. — Под ред. Р. Оссермана. — М.: Физматлит, 2003. — 352 с. Книга представляет собой обзор теории минимальных поверхностей, написанный ведущими специалистами в этой области. Рассматриваются вопросы полноты минимальных поверхностей, теория Неванлинны, краевые задачи для уравнения минимальных поверхностей и др. Для специалистов в области геометрии,...
Ленинград: ОНТИ - НКТП СССР, 1936. — 356 с. Книга известного немецкого математика Ф. Клейна (1849-1925). Подробно изложены основы проективной геометрии и теория проективных преобразований, необходимые для понимания дальнейших разделов книги. Далее показано, каким образом в проективную геометрию могут быть внесены понятия евклидовой геометрии; описываются соотношения, связывающие...
М.; Л: Государственное объединенное научно-техническое издательство, 1939. — 400 с. Книга выдающегося немецкого математика Ф.Х. Клейна (1849-1925) создана на основе лекций по высшей геометрии, прочитанных им в Гёттингенском университете и подготовленных к печати его учениками и последователями. Автор разделяет геометрию на две отдельные части: геометрия в ограниченной части...
Пер. с нем. — Изд. 2-е, стереотипное. — М.: Едиториал УРСС, 2004. — 400 с. — ISBN: 5-354-00603-1. Книга выдающегося немецкого математика Ф.Х. Клейна (1849-1925) создана на основе лекций по высшей геометрии, прочитанных им в Гёттингенском университете и подготовленных к печати его учениками и последователями. Автор разделяет геометрию на две отдельные части: геометрия в...
Перевод с англ. В.В. Батырева. — Под ред. В.А. Исковских. — М.: Мир, 1993. — 166 с. — ISBN 978-5-03-002393-3. Книга написана известными американскими и японским (С. Мори) математиками. (Первый автор знаком нашим читателям по его книге Мозаика теории комплексных кривых. М.: Мир, 1984). Она возникла из курса лекций на научном семинаре. В ней представлены: новые результаты в...
Ростов-на-Дону: Южный Федеральный Университет, 2014. – 160 с. – ISBN: 978-5-9275-1501-1.
Предлагаемая книга является систематическим изложением «оснований» теории деформаций регулярных поверхностей, в первую очередь теории изгибаний и бесконечно малых изгибаний. Несомненна её актуальность, поскольку последняя в мировой литературе подробная книга, посвящённая теории изгибаний,...
Навчальний посібник. — Харків: Харківський національний університет міського господарства імені О. М. Бекетова (ХНУМГ ім. О. М. Бекетова), 2019. — 172 с. — ISBN: 978-966-695-479-7. Стисле викладення класичних положень теорії кривих та поверхонь доповнено розглядом головних понять сферичної геометрії та тригонометрії з орієнтацією на геодезичні застосування. Увагу сконцентровано...
Учебник для педагогических институтов. — М.: Учпедгиз, 1946. — 301 с. Краткий исторический очерк. Абсолютная геометрия. Геометрия Евклида. Геометрия Лобачевского. Тригонометрия Лобачевского и абсолютная тригонометрия. Интерпретации геометрии Лобачевского. Теория площадей. Литература.
Под ред. В. Ф. Кагана. — Москва; Ленинград: Государственное издательство технико-теоретической литературы (ГИТТЛ), 1950. — 86 с. — (Геометрия Лобачевского и развитие ее идей, Выпуск 2). Настоящий второй выпуск серии «Геометрия Лобачевского и развитие ее идей» содержит две статьи, посвященные применению неевклидовой геометрии в механике и физике. Обе статьи были написаны еще до...
Пер. с нем. В.А. Залгаллера (ред.), Т.В. Хачатуровой. — М.: Наука, Главная редакция физико-математической литературы, 1985. — 336 с. Начальные сведения из теории выпуклых множеств излагаются во многих книгах по оптимизации и выпуклому анализу. Настоящая книга К. Лейхтвейса — написанный с геометрических позиций учебник. Здесь впервые в учебную литературу включены не только...
Перевод с французского В.В. Рыжкова. — М.: Мир, 1989. — 312 с. — (Современная математика. Вводные курсы). — ISBN: 5-03-001008-4. Монография учебного характера, написанная французским математиком на основе университетского курса лекций. Книга примыкает по тематике к известному двухтомнику М. Берже «Геометрия» (М.: Мир, 1984), но отличается от него простотой и доступностью....
Перевод, комментарии, вступительные статьи и примечания профессора В. Ф. Кагана. — Москва; Ленинград: Академия наук СССР, 1945. — 176 с. В.Ф. Каган Вступительные статьи Сочинения Н.И. Лобачевского, предшествовавшие геометрическим исследованиям Обзор сочинения «Геометрические исследования» Исследования Лежандра по теории параллельных линий Лобачевский Н.И. Геометрические...
М.: Изд-во АН СССР, 1956. — 598 с. — (Классики науки). В феврале 1956 года исполнилось сто лет со дня смерти великого русского математика Николая Ивановича Лобачевского и сто тридцать лет существования созданной им геометрической системы. В настоящее, юбилейное издание, выпускаемое в связи с этой датой, включены три сочинения Н. И. Лобачевского: «Геометрические исследования по...
Воронеж: Воронежский государственный архитектурно-строительный университет (ВГАСУ), 2012. — 142 с. В книге излагается разработанный автором коэффициентный подход к задаче описания однородных вложенных многообразий. Двумя основными составляющими такого подхода являются использование локальных канонических уравнений изучаемых многообразий и применение методов теории алгебр Ли....
Барнаул : АлтГПА, 2012. — 174 с. Учебное пособие написано в соответствии с программой курса геометрии для математических и физико-математических факультетов педагогических институтов по разделам Преобразования плоскости и Геометрические построения на плоскости. Пособие содержит также раздел Геометрические места точек, в котором значительное внимание уделено задачам на...
М.: МЦНМО, 2013. — 40 с. — ISBN: 978-5-4439-0612-3. Всякое одномерное семейство прямых на плоскости (кроме вырожденных случаев) является семейством касательных к некоторой кривой. В пространстве, однако, это уже совершенно не так; в брошюре объясняется, как, глядя на одномерное семейство прямых в пространстве, определить, является ли оно «касательным». По ходу дела читатель...
Учебное пособие. — М.: Государственное издательство технико-теоретической литературы (ГИТТЛ), 1956. — 212 с. Приводятся основные понятия и теоремы о выпуклых многогранниках. Одна из глав книги написана А.Д. Александровым и содержит его теорему о выпуклых многогранниках, из которой, как следствие, следует теорема Г. Минковского о том, что выпуклый многогранник определяется...
Учебное пособие. — Барнаул: Алтайский государственный педагогический университет (АлтГПУ), 2016. — 101 с. Учебное пособие написано на основе лекций, которые авторы читали в течение многих лет учащимся старших классов гимназий и лицеев г. Барнаула, Алейска, а также студентам-математикам АлтГПУ. Пособие состоит из трех разделов. В первом разделе излагается алгебраический подход к...
Учебное пособие. — Хабаровск: Тихоокеанский государственный университет (ТОГУ), 2020. — 143 с. — ISBN: 978-5-7389-3089-8. Учебное пособие написано к университетскому курсу геометрии. Рассмотрены вопросы теории, включены варианты заданий для самостоятельной работы по темам «Геометрия точечно-векторного пространства», «Аналитическая геометрия», «Геометрия аффинных...
Учебное пособие. — Калининград: БФУ им. И. Канта, 2011. — 155 с. — ISBN 978-5-9971-0163-3. Дано введение в математику фрактальных множеств, активно используемых в различных разделах современной математики и ее приложениях. Основное внимание уделяется изучению свойств фрактальных множеств, которые возникают как в различных ветвях чистой математики, так и в ее приложениях в науке...
Учебное пособие. — Томск: ТГУ, 2011. — 27 с. Учебное пособие посвящено свойствам простого отношения трех точек на аффинной прямой и двойного отношения четырех точек на проективной прямой, которые являются соответственно основными инвариантами аффинной и проективной геометрий. В нем методами аналитической геометрии подробно рассматриваются изменения значений этих отношений в...
М.: МЦНМО, 2004. — 234 с. Эта книга написана с целью дать доступное изложение теории h-принципа, лежащей на стыке между анализом и геометрией. Авторы излагают два метода доказательства h-принципа: голономную аппроксимацию и выпуклое интегрирование. Специальное внимание в книге уделено приложениям h-принципа в симплектической и контактной геометрии. Книга может быть основой...
Москва: Издательство МГУ, 1961. — 230 с. Книга предназначена для работы студентов в семинарах по геометрии в университетах и педагогических институтах. Книга может быть использована в качестве учебного пособия учителями математики средней школы для повышения квалификации. Наконец, многие разделы книги могут служить материалом для работы в школьных математических кружках под...
Конспект лекций. — Харьков: Харьковский национальный университет городского хозяйства (ХНУГХ) имени А.Н. Бекетова, 2016. — 79 с. В конспекте лекций изложен специальный раздел высшей математики «Основы сферической геометрии и тригонометрии», который имеет важное научное и практическое значение для специальности «Геодезия, картография, землеустройство». Базовые математические...
Мурманск: Мурманский государственный педагогический университет (МГПУ), 2008. — 273 с. Пособие содержит лекции по основному двухлетнему курсу геометрии, прочитанному студентам физико-математического факультета МПГУ. Геометрия - аксиоматическая наука. Поэтому данный курс геометрии есть продолжение школьного курса геометрии, в начале которого ( 6 класс) были сформулированы...
М.: МЦНМО, 2010. — 48 с. — ISBN 978-5-94057-647-1. Пучки, расслоения и их инварианты — это фундаментальные понятия современной геометрии, позволяющие исследовать глобальные свойства многообразий. Книга содержит основные определения и первые шаги этой теории. Подробно обсуждаются, в частности, когомологии со значениями в пучках и классы Черна расслоений. Книга является записью...
Казань: Казанский университет, 2020. — 73 с. В данном учебном пособии рассматриваются геометрия треугольника в трех аксиоматиках(геометрия Евклида, геометрия Лобачевского и геометрия Римана). В первой главе приведена историческая справка о зарождении неевклидовой геометрии,во второй главе пособия содержатся необходимые теоретические сведения (основные определения, свойства,...
Ярославль: ЯрГУ, 2012. — 104 с. — ISBN: 978-5-8397-0850-1. Материалы, содержащиеся в данном пособии, ознакомят студентов с основными понятиями, идеями и методами теории изображений, будут способствовать развитию у них пространственных представлений на основе геометрических чертежей. Основное внимание уделяется вопросам центрального и параллельного проецирований, полноте и...
М.: ГИТТЛ, 1956. — 530 с. В 1893 году, к столетнему юбилею со дня рождения Лобачевского, Казанское физико-математическое общество выпустило в свет сборник . Он содержал переводы шести важных работ, посвященных интерпретации геометрии Лобачевского и развитию его идей: две работы Бельтрами (об интерпретации неевклидовой геометрии и о пространствах постоянной кривизны), работы...
Москва: Государственное издательство технико-теоретической литературы, 1953. — 248 с. Цель настоящей книги — дать элементарное и вместе с тем систематическое и достаточно строгое изложение основ геометрии Лобачевского. Введение содержит краткий очерк возникновения геометрии Лобачевского, а первая глава — обзор аксиом абсолютной геометрии и ее основных теорем. Излагаются теория...
М.: Издательство Академии Наук СССР, 1961. — 312 с.: ил. Настоящая книга, выходящая в свет после смерти автора, академика Академии наук Эстонской ССР, профессора Юрия Юрьевича Нута (1892—1952), является существенным вкладом в имеющуюся уже богатую литературу о геометрии Лобачевского. Конечной целью академика Нута было создание новой теории пространства и времени, в значительной...
М.: Физматлит, 2008. — 368 c. В книге рассматриваются теоретические и практические аспекты самоподобных (фрактальных и мультифрактальных) случайных процессов и разработанные на их основе фрактальные и мультифрактальные модели самоподобного телекоммуникационного трафика. Приводится всесторонний анализ их эффективности. Авторы ориентируются на широкую аудиторию: студентов,...
Тюмень: ТюмГНГУ, 2011. ― 292 с. — ISBN 978-5-9961-0430-7. Излагаются элементы фрактальной геометрии: понятия фрактала и мультифрактала, размерности Хаусдорфа—Безиковича, Минковского, Реньи, построение фракталов как аттракторов системы итерированных подобий, аффинных, проективных и квадратичных кремо-новых преобразований, а также как образы булевых функций, свойства и методы...
Изд. 2-е, испр. — М.: Ленанд, 2016. — 352 с. — (Классический учебник МГУ.) — ISBN: 978-5-9710-2406-4. Книга основана на курсе лекций, которые с 2012 года читаются студентам механико-математического факультета МГУ им. М. В. Ломоносова. Этот курс лекций новый, в нем рассматриваются глубокие и важные вопросы, допускающие вместе с тем наглядное представление и неформальное...
Омск: ОмГТУ, 2015. — 92 с. — ISBN 978-5-8149-1953-3. Рассматриваются вопросы конструктивно-метрического образования кривых второго порядка в эллиптической плоскости, к которым в силу геометрической особенности - мнимости абсолюта этой плоскости - относятся окружность и эллипс. Конструктивные и метрические свойства кривых исследуются аналитическим методом, при этом эллиптическая...
2 -е издание, испр. — СПб.: Лань, 2015. — 240 c. Учебное пособие представляет собой краткое введение в ло кальную дифференциальную геометрию. Оно включает в себя кроме традиционных вопросов теории кривых и поверхностей в евклидовом пространстве необходимый алгебраический материал по линейным пространствам и отображениям, общей топологии, а также содержит основные факты...
М.: Наука, 1969. — 760 c. Теория выпуклых поверхностей — это раздел геометрии, где основные результаты за последние 25-30 лет получены советскими геометрами. Предлагаемая монография содержит изложение этих результатов. Она является как бы продолжением известной книги академика А. Д. Александрова «Внутренняя геометрия выпуклых поверхностей» (1948 г.). Чтение книги не...
М.: Наука. Главная редакция физико-математической литературы, 1983. — 288 с. Книга охватывает основные разделы геометрии для математических специальностей университетов и пединститутов. Она содержит аналитическую геометрию, теорию кривых и поверхностей, основания геометрии, в том числе проективную геометрию, и некоторые вопросы элементарной геометрии, в частности, вопросы...
Харьков: Издательство Харьковского университета, 1959. — 136 с. Книга содержит изложении курса 'Основания геометрии' в объеме, предусмотренном программой министерства высшего образования для университетов. Она отличается оригинальностью изложения многих разделов курса, в особенности раздела 'Геометрия Лобачевского' и раздела 'Проективная геометрия'.
2 изд. — Харьков: Издательство Харьковского университета, 1964. — 138 с. Книга содержит изложении курса 'Основания геометрии' в объеме, предусмотренном программой министерства высшего образования для университетов. Она отличается оригинальностью изложения многих разделов курса, в особенности раздела 'Геометрия Лобачевского' и раздела 'Проективная геометрия'. В настоящем издании...
М.: Наука, 1975. — 95 с.
Монография посвящена регулярному решению известной проблемы Минковского о существовании замкнутой выпуклой гиперповерхности с заданной гауссовой кривизной, а также ряду вопросов геометрии и теории дифференциальных уравнений с частными производными, примыкающих к этой проблеме. В частности, здесь рассматривается общая проблема существования замкнутой...
М.: Наука, Главная редакция физико-математической литературы, 1979. — 152 с. (OCR). Книга посвящена принципиальным вопросам, связанным с аксиоматическим построением евклидовой геометрии, геометрии Лобачевского, аффинной и проективной геометрий. В частности, в ней рассматриваются вопросы независимости, непротиворечивости и полноты системы аксиом указанных геометрий. Наряду с...
Учебно-методическое пособие для студентов физико - математического факультета. Елец, Елецкий государственный университет им. И.А. Бунина, 2005. - 51 с. Предлагаемое учебное пособие, написанное на основе университетского курса лекций. посвящено основаниям геометрии в традиционном смысле и примыкает по тематике к ряду известных пособий, но отличается от них простотой и доступностью....
3-е изд., перераб. и доп. — М.: Ленанд, 2015. — 128 с. Изложены основания геометрии Лобачевского, приведена система аксиом плоскости и пространства, подробно описаны наиболее известные модели геометрии Лобачевского — конформные модели А. Пуанкаре, проективные модели Кэли Клейна и Бельтрами. Рассмотрена реализация геометрии Лобачевского в псевдо-евклидовом пространстве....
Калининград: БФУ им. И. Канта, 2011. — 136 с. Пособие написано на основе лекций, прочитанных автором для студентов математического факультета Балтийского федерального университета им. И. Канта. Дан краткий исторический обзор обоснования геометрии. Общие вопросы аксиоматики (II глава) позволяют в дальнейшем (III—V главы) обоснованно вводить определения структур (геометрий),...
М.: Изд-во МЦНМО, 2004. – 89 с. (Векторный PDF, оглавление) Книга написана на основе курса лекций, читавшегося автором студентам первого курса Математического колледжа НМУ в осенних семестрах 1994-95,1995-96.1996-97 и 2002-03 учебных годов. Она содержит множество задач, предлагавшихся на семинарских занятиях. В книгу также включены полные тексты письменных экзаменов по этим...
М.: МЦНМО, 2014. — 88 с. — ISBN: 978-5-4439-2034-4. Книга написана на основе курса лекций, читавшегося автором студентам первого курса Математического колледжа НМУ в осенних семестрах 1994/95, 1995/96, 1996/97 и 2002/03 учебных годов. Она содержит множество задач, предлагавшихся на семинарских занятиях. В книгу также включены полные тексты письменных экзаменов по этим курсам, а...
5-е изд., стереотип. — М.: МЦНМО, 2016. — 88 с. — ISBN: 978-5-4439-0677-5. Книга написана на основе курса лекций, читавшегося автором студентам первого курса Математического колледжа НМУ в осенних семестрах 1994-95,1995-96.1996-97 и 2002-03 учебных годов. Она содержит множество задач, предлагавшихся на семинарских занятиях. В книгу также включены полные тексты письменных...
М.: Издательство Московского центра непрерывного математического образования, 2000. — 24 с. — Библиотека "Математическое просвещение", выпуск 4. Изогональное сопряжение относительно треугольника A 1 A 2 A 3 сопоставляет точке X такую точку Y, что прямая YA i симметрична прямой XA i относительно биссектрисы угла A i (i=1, 2, 3). Это преобразование обладает многими интересными...
2-е изд., перераб. и доп. — М.: МЦНМО, 2007. — 328 с. В книге дается систематическое изложение различных геометрий — евклидовой, аффинной, проективной, эллиптической, гиперболической, бесконечномерной. Проблемы различных геометрий рассматриваются с единой точки зрения, и всюду прослеживаются единые корни различных явлений. Все геометрические объекты исследуются с позиций...
2-е изд., доп. — М.: МЦНМО, 2015. — 147 с. Книга, адресованная студентам физико-математических специальностей, написана на основе лекций, прочитанных авторами в Независимом московском университете. В первой части изложены основы теории алгебраических кривых, рассматриваемых как римановы поверхности. Здесь преобладают сравнительно элементарные алгебраические и геометрические...
М.: ФАЗИС, 1999. — 142 с. — ISBN: 5-7036-0056-1. Библиотека студента-математика. Выпуск 7. Книга состоит из двух курсов лекций, прочитанных студентам Московского университета в весеннем семестре 1995 года. В первой части лекции В. В. Прасолова для студентов 1 курса, а во второй лекции О. В. Шварцмана для студентов 3 курса. Часть первая - Римановы поверхности и алгебраические...
Учебное пособие в 2-х частях. — Под ред. М.А. Князева. — Минск: Белорусский национальный технический университет (БНТУ), 2022. — 86 с. — ISBN 978-985-583-787-0 (Ч. 1). Данное пособие предназначено для студентов специальностей 1-36 01 05 «Машины и обработка металлов давлением», 1-36 01 06 «Оборудование и технология сварочного производства». Содержит задачи и вопросы по следующим...
Ръководство; Издателство- УАСГ- София; 2005 г.; 60 стр. на бълг. език. В ръководството са дадени основите на котиранана проекция. В началото е изяснен проекционният апарат и изобразяването на точки, прави и равнини. Разгледаниу са основните афинни и метрични задачи. Основна част от ръководството е отделена на изобразяването на тела: пирамиди, призми, цилиндри, конуси и сфери,...
Ръководство/учебно пособие/, издателство: УАСГ-София, 2005 г., 47 стр.
На български език.
В ръководството са дадени основите на монжовата проекция. В началото е изяснен проекционният апарат и изобразяването на точки, прави и равнини. След това е разгледан проблема за смяна на проекционния апарат, използването на помощни проекционни равнини и склопяване на равнина при...
Ръководство; Издателство: УАСГ - София; 2006 г.; 72 стр.
Ръководството е подходящо за всички технически ВУЗ, в които се изучава Дескриптивна геометрия.
Разгледани са три метода за изобразяване на равнинни сечения на тела:
- непосредствено - намиране на прободите на околните ръбове /образувателни/ на тялото и секущата равнина;
- допълнително ортогонално проектиране на тялото и...
М.: МЦНМО, 2009. — 32 с. — (Библиотека Математическое просвещение. Выпуск 36). — ISBN: 978-5-94057-539-9. В 1962 г. геометры Людвиг Данцер и Бранко Грюнбаум предложили выяснить, насколько много точек может содержать такое множество точек в n-мерном пространстве, любые три точки которого образуют остроугольный треугольник. Несложно придумать такое множество из 2n — 1 точки....
2-е издание, переработанное и дополненное. — М.: Физматлит, 2006. — 304 с. Книга предназначена для первоначального знакомства с геометрией поверхностей. Изложение доведено до разделов, имеющих важные приложения в механике, технике, оптике. Особенно наглядно применение полученных результатов в механике: на них опираются методы расчета упругих тонкостенных конструкций. Также в...
Монография. — М.: Наука. Главная редакция физико-математической литературы, 1966. — 648 с.: ил. Книга рассчитана на студентов университетов и педагогических институтов, научных работников, учителей и инженеров, интересующихся геометрией. Книга предполагает знакомство с курсами аналитической геометрии и высшей алгебры, а также с основными понятиями теории групп (в объеме первых...
Учебное пособие по спецкурсу для студентов-математиков педагогических специальностей вузов. - Саратов: Издательство "Научная книга", 2008. - 279 с.
Книга адресована студентам математических специальностей вузов, предназначена в качестве учебного пособия по специальным курсам, посвященным вопросам неевклидовых геометрий. Может быть использована учителями средних школ при...
Учебно-методическое пособие для преподавателей, аспирантов и студентов математических специальностей вузов. – Саратов: СГУ, 2009. – 49с.
Учебно-методическое пособие адресовано преподавателям, аспирантам и студентам математических специальностей вузов, интересующимся вопросами неевклидовых геометрий. Пособие содержит большое количество задач исследовательского характера, которые...
Учебное пособие. - Саратов, 2012. - 22 с.
Учебное пособие адресовано преподавателям, аспирантам и студентам вузов, интересующимся вопросами неевклидовых геометрий. В пособии введено понятие многореберника плоскости с проективной метрикой Кэли-Клейна, обобщающее понятия многоугольника и n-контура, на основе которого дано понятие конечного многогранника в копсевдоевклидовом...
Томск: Красное знамя, 1938. — 434 с. В 1-й части настоящей работы проводится систематическое исследование замечательных кривых, выводятся их уравнения в различных системах координат, подробно исследуются особенности их форм, исследуются геометрические и механические свойства этих кривых, вычисляются их элементы, излагаются различные способы их построения. как графические, так и...
Москва: Инфра-М, 2023. — 142 с. — (Научная мысль). — ISBN 978-5-16-011910-6. В монографии исследуется поверхность, образованная двумя семействами окружностей — циклида Дюпена, названная так в честь открывшего ее великого французского ученого Пьера Шарля Франсуа Дюпена, ученика Гаспара Монжа. Рассматриваются свойства циклиды Дюпена, ее приложение к различным геометрическим...
М.: Физматлит, 2007. — x + 242 с. Первая монография на русском языке об инвариантных управляемых системах на группах Ли и их проекциях на однородные пространства. Рассматриваются следующие задачи: глобальная управляемость правоинвариантных систем на группах Ли, в особенности на разрешимых группах Ли; управляемость билинейных систем в ортанте; симметрии инвариантных...
М.: Лань, 2019. — 180 с. В настоящем учебном пособии помещены работы, посвященные исследованиям в области фрактальной геометрии, находящей в настоящее время многочисленные приложения — в физике, экономике, педагогике, нанотехнологиях и других областях. Особое внимание автор уделяет методике изучения фрактальной геометрии и разработке многоэтапных математико-информационных...
М.: Мир, 1986. — 168 с. Небольшая книга английского математика, содержащая доступное изложение современных результатов в данной области. Автор приводит большое число примеров и иллюстраций, указывает связи полученных результатов геометрии и топологии с другими областями математики. Для математиков разных специальностей и специалистов по теоретической физике. От редактора...
2-е изд., испр. и доп. –– М.: МЦНМО, 2018. –– 56 с. Брошюра написана по материалам цикла лекций, прочитанных автором участникам Летней школы «Современная математика» в Дубне 20 - 26 июля 2008 г. В ней излагается классификация правильных многогранников в евклидовом пространстве произвольной размерности. Попутно читатель знакомится с такими важными алгебраическими понятиями, как...
Москва; Ленинград: Государственное издательство технико-теоретической литературы (ГИТТЛ), 1951. — 189 с. — (Геометрия Лобачевского и развитие ее идей, Выпуск 3). Работа А.С. Смогоржевского в значительной мере оригинальна. Помимо нового подхода к некоторым вопросам самой гиперболической геометрии во вступительных главах и некоторых удачно отмеченных новых теорем, автором найдены...
Перевод с англ. Б.Р. Френкина. — М.: МЦНМО, 2017. — 263 с. — ISBN: 978-5-4439-1168-7. Эта книга, основанная на лекциях, читавшихся автором на первом курсе Независимого московского университета, представляет собой введение в евклидову, сферическую, проективную и гиперболическую (Лобачевского) геометрию, написанное в синтетическом, бескоординатном стиле; по ходу дела читатель...
Электронное издание. — Перевод с англ. Б.Р. Френкина. — М.: МЦНМО, 2018. — 262 с. — ISBN: 978-5-4439-3168-5. True PDF Эта книга, основанная на лекциях, читавшихся автором на первом курсе Независимого московского университета, представляет собой введение в евклидову, сферическую, проективную и гиперболическую (Лобачевского) геометрию, написанное в синтетическом, бескоординатном...
Издательство: Independetn University of Moscow, 2011, 160 стр.
Данная брошюра является расширенным вариантом лекций по курсу "Геометрия", прочитанным автором осенью 2003 года в Независимом Московском Университете. Книга написана на английском языке, что, по задумке автора, поможет будущим математикам приобщиться к международной математической культуре. Каждая лекция снабжена...
Учебно-методическое пособие. — Казань: Казанский федеральный университет (КФУ), 2015. — 98 с. Данное учебно-методическое пособие включает минимум вводного курса и некоторые приложения метрической геометрии. Оно предназначено для студентов-математиков III-IV курсов и рассчитано на 36 часов аудиторной нагрузки с учетом выбора тем преподавателем. Метрическая геометрия имеет много...
Учебно-методическое пособие. — Казань: Казанский университет, 2016. — 52 с. Пособие содержит введение в риманову геометрию. Предназначено для студентов-математиков III-IV курсов. Введение. Связность на многообразии. Ковариантное дифференцирование. Параллельный перенос вектора вдоль кривой. Группа голономии. Геодезические линейной связности. Экспоненциальное отображение....
Часть 1: Учебно-методическое пособие. - Казань: Казанский федеральный университет, 2012. - 38 с.
Данное учебно-методическое пособие включает минимум вводного курса по геометрии Лобачевского и ее применению в специальной теории относительности (СТО). Оно предназначено для студентов математиков старших курсов университетов, магистрантов и рассчитано на 16 часов лекций, 20 часов...
Оқу құралы. — Астана: Фолиант, 2008. — 88 б. Оқу құралы «Математика» мамандығы студенттерінің геометрия пәнінен алған білімдерін бақылау, бағалауға арналған тест тапсырмаларынан қүралған. Жинақ педагогикалық, гуманитарлық колледждердегі 0303002 «Математика» мамандығының студенттеріне арналған.
Перевод с немецкого Н.М. Макаровой. — Редакция перевода, приложения и примечания И. М. Яглома. — М.: Государственное издательство физико-математической литературы, 1958. — 363 c. Эта книга известного венгерского математика посвящена разнообразным задачам о плотнейшем расположении фигур или тел, а также некоторым смежным вопросам, связанным с этими задачами. Книга содержит...
Вінниця: Вiнницький державний педагогiчний унiверситет iменi Михайла Коцюбинського, 2006. — 159 c. Даний збірник задач складений у відповідності до діючої програми з геометрії для математичних спеціальностей педагогічних університетів. Задачником можуть користуватись не тільки студенти стаціонарного відділення, але й заочного та особи, які вивчають предмет самостійно.
Рукопис. Вінниця, 2005. - 116 с.
Даний конспект містить 24 лекції для студентів заочної форми навчання спеціальності "Математика" зі всього курсу геометрії. В лекціях дається план лекції, наводяться основні формули та формулювання теорем. Розглядаються приклади. Лекції охоплюють такі розділи: векторна алгебра, аналітична геометрія на площині та в просторі, перетворення площини...
Вінниця, 2012. - 104 с. Курс конструктивної геометрії включає розділи: Геометричні побудови на площині. Проективна геометрія. Методи зображень. В задачах на побудову мова йде про побудови геометричних фігур заданими засобами "- зазвичай, за допомогою циркуля і лінійки. При цьому маємо на увазі ідеальні побудови. Крім побудов циркулем і лінійкою, розглядаються побудови за...
Вінниця, 2011. - 70 с.
Під "основами геометрії" завжди розуміють систему аксіом геометрії Евкліда разом з питаннями несуперечності, повноти і незалежності аксіом - особливо аксіоми паралельності.
У першому розділі "Історичний огляд обґрунтування геометрії" розглянуто історичну послідовність розвитку геометричних ідей, геометрію до Евкліда, "Початки" Евкліда, критика системи...
М.: Наука. Гл. ред. физ.-мат. лит. 1991.— 176 с. — ISBN: 5-02-014811-3. — (Совр. мат. для студентов). В популярной форме рассказывается об одном из самых интригующих разделов современной геометрии — о минимальных поверхностях в трехмерном пространстве. Такие поверхности моделируют границы раздела физических сред с одинаковыми давлениями и возникают в самых разных областях...
Учебное пособие. — Горно-Алтайск: Горно-Алтайский государственный университет (ГАГУ), 2022. — 59 с. Пособие предназначено в первую очередь студентам-математикам ГАГУ, изучающим курс «Теория римановых поверхностей». В нём рассматриваются вопросы, касающиеся в основном методов построения римановых поверхностей многозначных функций, поиска точек ветвления для таких функций и...
Монография. — Петроград: Сеятель, 1922. — 177 c. Предисловие Введение Основные предложения гиперболической геометрии Предложения, лежащие в основе вывода формул гиперболической тригонометрии Вывод формул неевклидовой тригонометрии Вывод тригонометрических формул из рассмотрения бесконечно-малых фигур Элементы аналитической геометрии Изменение длин дуг и площадей в неевклидовой...
Пер. с англ. Ю.А. Данилов, А. Шкуров. — М.: Мир, 1991. — 264 с. — ISBN 5-03-001712-7. В книге известного норвежского физика дается ясное и простое изложение математических свойств фракталов и описываются приложения теории фракталов в гидродинамике, океанологии, гидрологии, в исследовании перколяционных процессов и пр. Для желающих ознакомиться с теорией фракталов и применять ее...
Ленинград: Наука, 1979. — 272 с. Публикуемая в настоящем издании монография гениального русского кристаллографа академика Евграфа Степановича Федорова «Правильное деление плоскости и пространства» была первоначально издана в 1899 г., в Германии на немецком языке под названием «Regulare Plan- und Raum-teilung» в трудах Баварской Академии наук в ознаменование избрания Е. С....
Учебное пособие. — М.: Просвещение, 1965. — 239 с. В книге рассматриваются вопросы: абсолютная геометрия, осуществление евклидовой геометрии в параболической сети сфер, осуществление геометрии Лобачевского-Больяи в гиперболической сети сфер и эллиптической геометрии Римана в эллиптической сети сфер. Сделаны общие выводы о геометрии реального пространства. Пособие подготовлено в...
Санкт-Петербург, 1804. — 94 с. Рассечение Конуса плоскостью. О кривых линиях. О круге. О эллипсе. О параболе. О гиперболе. Геометрические построения. Таблицы.
М.: Наука, 1966. — 416 с. Настоящая книга объединяет материал различных лекционных курсов, посвященных теории объемов, изопериметрическим проблемам, теории выпуклых тел и общей интегральной геометрии, которые автор читал в Бернском университете. За исключением отдельных лекций специального характера, эти курсы соответствовали учебной программе общеrо введения в высшую...
М.: Наука, 1965. — 171 с. — (Математическая библиотечка). Эта книга вовсе не является систематическим курсом комбинаторной геометрии. Авторы выбрали из этого раздела математики несколько вопросов, в основной своей части концентрирующихся вокруг знаменитой теоремы Хелли и проблемы Борсука. Книгу вполне можно рассматривать как "задачник" с задачами на доказательства,...
Пер. с анг. — М.: Мир, 1985. — 343 с. Книга американского специалиста, дающая картину взаимодействия разных областей математики с современной теоретической физикой. Она охватывает результаты недавних исследований по геометрическому квантованию и его применениям в квантовой статистической механике и квантовой теории поля; материал подан в компактной и доступной форме. Для...
Учебное пособие. — Самарканд: Самаркандский государственный университет им. Алишера Навои, 1972. — 124 с. Книга Ф. Клейна "Неевклидова геометрия", богатая многими идеями, давно стала библиографической редкостью. В настоящее время ощущается настоятельная необходимость в ее переиздании. Предлагаемая вниманию читателей книга, в которой на базе вырождающихся мероопределений...
Монография. — М.: Сам Полиграфист, 2020. — 92 с. — ISBN: 978-5-00166-032-3. В книге рассмотрен аналитический метод нахождения замечательных центров, линий и поверхностей треугольника и тетраэдра в модели Бельтрами пространства Лобачевского. Используются простой математический аппарат, опирающийся на решения цепочки систем трех линейных уравнений (происходящих из линейных...
Пер. с англ. А.И. Гарбера [и др.]; под ред. Н.П. Долбилина; с прил. В.М. Бухштабера, Н.Ю Ероховца, Т.Е. Панова. — М.: МЦНМО, 2014. — 568 с. — ISBN: 978-5-4439-0123-7. Книга представляет собой одно из лучших изложений современного состояния комбинаторной теории выпуклых многогранников, принадлежащее крупному немецкому математику. Изложение сопровождается богатым набором задач,...
Барнаул: Издательство Алтайского государственного университета, 1999. - 58 с.
Учебное пособие для студентов математического факультета. В пособии излагаются основные исторические факты и приводятся результаты по основаниям геометрии. Большой подбор упражнений и задач делает пособие удобным для самостоятельной работы студентов.
Барнаул: Издательство Алтайского государственного университета, 1997. - 81 с.
Даются необходимые сведения из геометрии римановых многообразий. Большой подбор упражнений и задач делает пособие удобным для самостоятельной работы студентов.
Учебник-първо издание, издателство: Наука и изкуство, гр. София, България, 1992 г., 388 стр. На български език В учебника са изложени подробно най-съществените въпроси за главните проекционни методи на дескриптивната геометрия – монжовата проекция, котираната проекция, аксонометрията, перспективата и техните приложения. Учебникът е предназначен за студентите от Висш институт по...
Учебно-методическое пособие. Казанский государственный университет им. В.И. Ульянова-Ленина, 2002. - 106 с. Практика показывает, что студенты младших курсов мехмата обычно испытывают определенные затруднения с выбором тем курсовых работ. Для того, чтобы облегчить им эту задачу и написано настоящее пособие. Оно подготовлено преподавателями кафедры геометрии Казанского...
Учебник. — Пермь: Пермский государственный гуманитарно-педагогический университет (ПГГПУ), 2013. — 188 с. Учебник составлен в соответствии с требованиями Федерального государственного образовательного стандарта высшего профессионального образования по направлению «Педагогическое образование» и предназначен для изучения одноименной дисциплины. Дисциплина «Геометрические...
2-е изд. — М.: Наука, 1983. — 80 с. Постулаты параллельности Евклида и Лобачевского и их связь с вопросом о сумме углов треугольника и вопросом о существовании подобных фигур. Параллельные прямые и их простейшие свойства. Основные свойства пересекающихся, расходящихся и параллельных прямых... Постулаты Евклида и Лобачевского Сумма углов треугольника Дефект треугольника и...
Москва; Ленинград: Государственное издательство технико-теоретической литературы, 1950. — 148 с. — (Геометрия Лобачевского и развитие ее идей, Выпуск 1). Настоящий выпуск содержит две статьи, посвященные строению геометрии Лобачевского. Конечно, этим слишком много сказано. Формы и методы строения неевклидовой геометрии, развернутые в течение 125 лет со времени ее открытия,...
М.: МИСиС, 2019. — 270 с. — ISBN: 978-5-906953-91-9. Учебник представляет собой изложение курса «Фрактальная геометрия», преподаваемого студентам третьего курса бакалавриата. Курс посвящен системам итерированных преобразований и понятию детерминированного аттрактора. В учебнике изложены базовые понятия, основные определения и теоремы. Приведены доказательства основных теорем....
Миниатюры из бесконечного рая. – Нью-Йорк:; Ижевск: НИЦ "Регулярная и хаотическая динамика", 2001. – 528 с. Основная цель книги — помочь читателю глубже понять, что такое самоподобие — возможно, наиболее важную из встречающихся в природе симметрии, а также продемонстрировать широчайший диапазон применений масштабной инвариантности в физике, химии, биологии, музыке и, в...
С.-Петербург: Типография Морского Министерства, 1893. — 144 с. Настоящий труд имеет целью изложение курсов сферической геометрии и сферической тригонометрии для воспитанников Морского Кадетского Корпуса по программе, утвержденной начальством корпуса в Марте 1891 г. Сферическая геометрия. Понятие о поверхностях вращения. Сферическая поверхность. Касательная к кривым линиям....
2-е издание, стереотипное. — М.: Едиториал УРСС, 2004. — 192 с. Настоящее издание в доступной форме знакомит читателя с кругом вопросов, связывающих учение о комплексных числах с геометрией. Автор рассматривает разнородные геометрические теоремы, доказываемые с использованием разных типов комплексных чисел. Дается также краткое изложение вопроса о применениях аппарата комплексных...
М.: Физматгиз, 1963. — 193 с. Настоящее издание в доступной форме знакомит читателя с кругом вопросов, связывающих учение о комплексных числах с геометрией. Автор рассматривает разнородные геометрические теоремы, доказываемые с использованием разных типов комплексных чисел. Дается также краткое изложение вопроса о применениях аппарата комплексных чисел в геометрии Лобачевского....
М.; Л.: Государственное издательство технико-теоретической литературы, 1951. — 344 с. — (Библиотека математического кружка. Выпуск 4). Эта книга посвящена некоторым задачам из общей теории выпуклых тел (определение выпуклого тела см. в тексте, стр. 13 и 29). Созданная в конце прошлого века теория выпуклых тел в настоящее время является наукой, богатой общими методами и отдельными...
Уважаемые администратор, модераторы и доверенные пользователи.Я хочу предложить Вам в разделе Высшая геометрия создать новый подраздел Дифференциальная геометрия, которая является самостоятельной областью математики. Дифференциальная геометрия, раздел геометрии, в котором свойства кривых, поверхностей и других геометрических многообразий изучаются методами математического анализа, в первую очередь – дифференциального исчисленияНиже представлена некоторая часть литературы для нового подраздела. А также у меня имеется несколько десятков книг по этой теме, которые я буду постепенно добавлять....
Уважаемые: Администратор, модераторы и доверенные пользователи.Друзья, я предлагаю в разделе Высшая геометрия создать новый подраздел Алгебраическая геометрия, которая является самостоятельной областью (направлением, ветвью) математики - Высшей геометрии:Это соответствует требованиям мировых и официальных стандартов, изложенных в Википедии:1.Википедия (Алгебраическая геометрия): "Алгебраическая геометрия — раздел математики, который объединяет алгебру и геометрию".2.Википедия (Категория: Алгебраическая геометрия): "Алгебраическая геометрия — это раздел математики, где алгебра, используемая для решения систем полиномиальных уравнений от многих переменных, встречается с геометрией кривых, поверхностей и алгебраических многообразий более высокой размерности".3.Википедия (Геометрия): "Алгебраическая геометрия — изучает алгебраические многообразия (то есть множества, которые задаются полиномиальными уравнениями) с помощью методов современной общей алгебры". Вывод: Современная геометрия включает в себя следующие разделы (инструментальные подразделы, по используемым методам):Алгебраическая геометрия.Литература для переноса в новый подраздел Алгебраическая геометрия: ...С уважением, благодарностью и благословением,
Комментарии
Вывод: Современная геометрия включает в себя следующие разделы (инструментальные подразделы, по используемым методам): Алгебраическая геометрия.Литература для переноса в новый подраздел Алгебраическая геометрия:
...С уважением, благодарностью и благословением,
Я благодарен Вам за добавление подраздела Алгебраическая геометрия.
С уважением,
/file/345431/
/file/447569/
/file/89971/
/file/60457/
/file/45728/
/file/1411804/
/file/519840/
/file/633781/
/file/442274/
/file/342671/
/file/192638/
неизвестная ссылка
/file/109709/
/file/1589567/
/file/1173319/
/file/991356/
/file/714094/
/file/636455/
/file/575793/
/file/429906/
/file/370350/
/file/12988/
/file/1494305/
/file/1391837/
/file/905476/Предлагаю в разделе Геометрия создать подраздел Стереометрия, учитывая критерии создания названий разделов и подразделов .
/file/447581/
/file/462081/
/file/464587/
/file/515465/
/file/918595/
/file/1145306/
/file/1235632/
/file/452959/
/file/897711/
/file/444813/
/file/353729/
/file/1255717/
/file/1260659/
/file/192639/
/file/201407/
/file/236666/
/file/274265/
/file/648250/
/file/1093619/
/file/1440044/
/file/66110/
/file/72588/
/file/353684/
/file/1002252/