Elementary Geometry In Hyperbolic Space
DOWNLOAD
Download Elementary Geometry In Hyperbolic Space PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Elementary Geometry In Hyperbolic Space book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Elementary Geometry In Hyperbolic Space
DOWNLOAD
Author : Werner Fenchel
language : en
Publisher: Walter de Gruyter
Release Date : 1989
Elementary Geometry In Hyperbolic Space written by Werner Fenchel and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Hyperbolic geometry is in a period of revised interest. This book contains a substantial account of the parts of the theory basic to the study of Kleinian groups, but it also contains the more broad-reaching thoughts of the author, one of the pioneers in the theory of convex bodies and a major contributor in other fields of mathematics. Annotation copyrighted by Book News, Inc., Portland, OR
Hyperbolic Geometry
DOWNLOAD
Author : James W. Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Hyperbolic Geometry written by James W. Anderson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. This updated second edition also features: - an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; - the hyperboloid model of the hyperbolic plane; - a brief discussion of generalizations to higher dimensions; - many new exercises.
Lectures On Hyperbolic Geometry
DOWNLOAD
Author : Riccardo Benedetti
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Hyperbolic Geometry written by Riccardo Benedetti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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 far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory. A large part is devoted to the three-dimensional case: a complete and elementary proof of the hyperbolic surgery theorem is given based on the possibility of representing three manifolds as glued ideal tetrahedra. The last chapter deals with some related ideas and generalizations (bounded cohomology, flat fiber bundles, amenable groups). This is the first book to collect this material together from numerous scattered sources to give a detailed presentation at a unified level accessible to novice readers.
Foundations Of Hyperbolic Manifolds
DOWNLOAD
Author : John Ratcliffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.
A Simple Non Euclidean Geometry And Its Physical Basis
DOWNLOAD
Author : Isaak Moiseevic Jaglom
language : en
Publisher:
Release Date : 1979
A Simple Non Euclidean Geometry And Its Physical Basis written by Isaak Moiseevic Jaglom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
A Gyrovector Space Approach To Hyperbolic Geometry
DOWNLOAD
Author : Abraham A. Ungar
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2009
A Gyrovector Space Approach To Hyperbolic Geometry written by Abraham A. Ungar and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry
Elementary Geometry
DOWNLOAD
Author : Ilka Agricola
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Elementary Geometry written by Ilka Agricola and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Elementary Differential Geometry
DOWNLOAD
Author : A.N. Pressley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Elementary Differential Geometry written by A.N. Pressley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times. Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there. The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecturers, and for all others interested in the subject. Andrew Pressley is Professor of Mathematics at King’s College London, UK. The Springer Undergraduate Mathematics Series (SUMS) is a series designed for undergraduates in mathematics and the sciences worldwide. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully worked solutions.
Fundamentals Of Hyperbolic Manifolds
DOWNLOAD
Author : R. D. Canary
language : en
Publisher: Cambridge University Press
Release Date : 2006-04-13
Fundamentals Of Hyperbolic Manifolds written by R. D. Canary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Mathematics categories.
Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.
Topics In Geometry
DOWNLOAD
Author : Robert Bix
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Topics In Geometry written by Robert Bix and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered.The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.