Elementary Geometry In Hyperbolic Space
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Author | : Werner Fenchel |
Publisher | : Walter de Gruyter |
Total Pages | : 241 |
Release | : 2011-04-20 |
Genre | : Mathematics |
ISBN | : 3110849453 |
Download Elementary Geometry in Hyperbolic Space Book in PDF, Epub and Kindle
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.
Author | : Ilka Agricola |
Publisher | : American Mathematical Soc. |
Total Pages | : 257 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821843478 |
Download Elementary Geometry Book in PDF, Epub and Kindle
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.
Author | : Silvio Levy |
Publisher | : Cambridge University Press |
Total Pages | : 212 |
Release | : 1997-09-28 |
Genre | : Mathematics |
ISBN | : 9780521629621 |
Download Flavors of Geometry Book in PDF, Epub and Kindle
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.
Author | : Riccardo Benedetti |
Publisher | : Springer Science & Business Media |
Total Pages | : 343 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642581587 |
Download Lectures on Hyperbolic Geometry Book in PDF, Epub and Kindle
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.
Author | : James W. Anderson |
Publisher | : Springer Science & Business Media |
Total Pages | : 239 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1447139879 |
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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
Author | : John Stillwell |
Publisher | : American Mathematical Soc. |
Total Pages | : 172 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9780821809228 |
Download Sources of Hyperbolic Geometry Book in PDF, Epub and Kindle
Presents the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics.
Author | : Arlan Ramsay |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475755856 |
Download Introduction to Hyperbolic Geometry Book in PDF, Epub and Kindle
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.
Author | : Birger Iversen |
Publisher | : CUP Archive |
Total Pages | : 322 |
Release | : 1992-12-17 |
Genre | : Mathematics |
ISBN | : 9780521435284 |
Download Hyperbolic Geometry Book in PDF, Epub and Kindle
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.
Author | : D. B. A. Epstein |
Publisher | : CUP Archive |
Total Pages | : 340 |
Release | : 1987-03-19 |
Genre | : Mathematics |
ISBN | : 9780521339063 |
Download Analytical and Geometric Aspects of Hyperbolic Space Book in PDF, Epub and Kindle
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.
Author | : Francis Bonahon |
Publisher | : American Mathematical Soc. |
Total Pages | : 403 |
Release | : 2009-07-14 |
Genre | : Mathematics |
ISBN | : 082184816X |
Download Low-Dimensional Geometry Book in PDF, Epub and Kindle
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.