Elementary Geometry In Hyperbolic Space

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Elementary Geometry in Hyperbolic Space

Werner Fenchel
Elementary Geometry in Hyperbolic Space Book PDF

Author : Werner Fenchel
Publisher : Walter de Gruyter
Page : 241 pages
File Size : 46,6 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110849455

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Elementary Geometry in Hyperbolic Space by Werner Fenchel Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Elementary Geometry

Ilka Agricola,Thomas Friedrich
Elementary Geometry Book PDF

Author : Ilka Agricola,Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 257 pages
File Size : 44,6 Mb
Release : 2008
Category : Geometry
ISBN : 9780821843475

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Elementary Geometry by Ilka Agricola,Thomas Friedrich Pdf

Plane geometry is developed from its basic objects and their properties and then moves to conics and basic solids, including the Platonic solids and a proof of Euler's polytope formula. Particular care is taken to explain symmetry groups, including the description of ornaments and the classification of isometries.

Hyperbolic Geometry

James W. Anderson
Hyperbolic Geometry Book PDF

Author : James W. Anderson
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 49,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781447139874

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Hyperbolic Geometry by James W. Anderson Pdf

Thoroughly updated, featuring new material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity Includes full solutions for all exercises Successful first edition sold over 800 copies in North America

The Shape of Space

Jeffrey R. Weeks
The Shape of Space Book PDF

Author : Jeffrey R. Weeks
Publisher : CRC Press
Page : 263 pages
File Size : 54,7 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781135542658

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The Shape of Space by Jeffrey R. Weeks Pdf

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

Flavors of Geometry

Silvio Levy
Flavors of Geometry Book PDF

Author : Silvio Levy
Publisher : Cambridge University Press
Page : 212 pages
File Size : 55,9 Mb
Release : 1997-09-28
Category : Mathematics
ISBN : 0521629624

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Flavors of Geometry by Silvio Levy Pdf

Flavors of Geometry is a volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. Growing out of a series of introductory lectures given at the Mathematical Sciences Research Institute in January 1995 and January 1996, the book presents chapters by masters in their respective fields on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation. Each lecture begins with a discussion of elementary concepts, examines the highlights of the field, and concludes with a look at more advanced material. The style and presentation of the chapters are clear and accessible, and most of the lectures are richly illustrated. Bibiliographies and indexes are included to encourage further reading on the topics discussed.

Lectures on Hyperbolic Geometry

Riccardo Benedetti,Carlo Petronio
Lectures on Hyperbolic Geometry Book PDF

Author : Riccardo Benedetti,Carlo Petronio
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581588

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Lectures on Hyperbolic Geometry by Riccardo Benedetti,Carlo Petronio Pdf

Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.

Low-Dimensional Geometry

Francis Bonahon
Low Dimensional Geometry Book PDF

Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 49,6 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9780821848166

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Low-Dimensional Geometry by Francis Bonahon Pdf

The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

Geometry, Topology and Dynamics of Character Varieties

William Goldman
Geometry Topology and Dynamics of Character Varieties Book PDF

Author : William Goldman
Publisher : World Scientific
Page : 362 pages
File Size : 54,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814401364

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Geometry, Topology and Dynamics of Character Varieties by William Goldman Pdf

This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

Elements of Asymptotic Geometry

Sergei Buyalo,Viktor Schroeder
Elements of Asymptotic Geometry Book PDF

Author : Sergei Buyalo,Viktor Schroeder
Publisher : European Mathematical Society
Page : 220 pages
File Size : 41,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190361

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Elements of Asymptotic Geometry by Sergei Buyalo,Viktor Schroeder Pdf

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 encoded in the boundary at infinity. In the first part of this book, in analogy with the concepts of classical hyperbolic geometry, the authors provide a systematic account of the basic theory of Gromov hyperbolic spaces. These spaces have been studied extensively in the last twenty years and have found applications in group theory, geometric topology, Kleinian groups, as well as dynamics and rigidity theory. In the second part of the book, various aspects of the asymptotic geometry of arbitrary metric spaces are considered. It turns out that the boundary at infinity approach is not appropriate in the general case, but dimension theory proves useful for finding interesting results and applications. The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory. The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich.

A Simple Non-Euclidean Geometry and Its Physical Basis

I.M. Yaglom
A Simple Non Euclidean Geometry and Its Physical Basis Book PDF

Author : I.M. Yaglom
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261353

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A Simple Non-Euclidean Geometry and Its Physical Basis by I.M. Yaglom Pdf

There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. 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-Euclidean, Hyperbolic Plane

P. Kelly,G. Matthews
The Non Euclidean Hyperbolic Plane Book PDF

Author : P. Kelly,G. Matthews
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461381259

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The Non-Euclidean, Hyperbolic Plane by P. Kelly,G. Matthews Pdf

The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery.

Hyperbolic Geometry

Birger Iversen
Hyperbolic Geometry Book PDF

Author : Birger Iversen
Publisher : Cambridge University Press
Page : 317 pages
File Size : 55,5 Mb
Release : 1992-12-17
Category : Mathematics
ISBN : 9780521435086

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Hyperbolic Geometry by Birger Iversen Pdf

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.

Analytical and Geometric Aspects of Hyperbolic Space

D. B. A. Epstein
Analytical and Geometric Aspects of Hyperbolic Space Book PDF

Author : D. B. A. Epstein
Publisher : CUP Archive
Page : 340 pages
File Size : 41,8 Mb
Release : 1987-03-19
Category : Mathematics
ISBN : 0521339065

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Analytical and Geometric Aspects of Hyperbolic Space by D. B. A. Epstein Pdf

This work and its companion volume form the collected papers from two symposia held at Durham and Warwick in 1984. Volume I contains an expository account by David Epstein and his students of certain parts of Thurston's famous mimeographed notes. This is preceded by a clear and comprehensive account by S. J. Patterson of his fundamental work on measures on limit sets of Kleinian groups.

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

Tushar Das,David Simmons,Mariusz Urbański
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces Book PDF

Author : Tushar Das,David Simmons,Mariusz Urbański
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 53,6 Mb
Release : 2017-04-14
Category : Geometry, Hyperbolic
ISBN : 9781470434656

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Geometry and Dynamics in Gromov Hyperbolic Metric Spaces by Tushar Das,David Simmons,Mariusz Urbański Pdf

This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Introduction to Hyperbolic Geometry

Arlan Ramsay,Robert D. Richtmyer
Introduction to Hyperbolic Geometry Book PDF

Author : Arlan Ramsay,Robert D. Richtmyer
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 45,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475755855

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Introduction to Hyperbolic Geometry by Arlan Ramsay,Robert D. Richtmyer Pdf

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 without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.