Introductory Non Euclidean Geometry

Author : Henry Parker Manning
Publisher : Courier Corporation
Page : 110 pages
File Size : 43,8 Mb
Release : 2005-02-18
Category : Mathematics
ISBN : 9780486442624

Get Book

Introductory Non-Euclidean Geometry by Henry Parker Manning Pdf

This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. Major topics include hyperbolic geometry, single elliptic geometry, and analytic non-Euclidean geometry. 1901 edition.

Author : Harold Scott Macdonald Coxeter
Publisher : Unknown
Page : 0 pages
File Size : 51,7 Mb
Release : 1965
Category : Geometry, Non-Euclidean
ISBN : LCCN:98085640

Get Book

Non-Euclidean geometry by Harold Scott Macdonald Coxeter Pdf

Author : Harold E. Wolfe
Publisher : Courier Corporation
Page : 272 pages
File Size : 53,6 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486320373

Get Book

Introduction to Non-Euclidean Geometry by Harold E. Wolfe Pdf

College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry. Numerous exercises. 1945 edition.

Author : EISENREICH
Publisher : Elsevier
Page : 287 pages
File Size : 46,7 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295312

Get Book

Introduction to Non-Euclidean Geometry by EISENREICH Pdf

An Introduction to Non-Euclidean Geometry covers some introductory topics related to non-Euclidian geometry, including hyperbolic and elliptic geometries. This book is organized into three parts encompassing eight chapters. The first part provides mathematical proofs of Euclid’s fifth postulate concerning the extent of a straight line and the theory of parallels. The second part describes some problems in hyperbolic geometry, such as cases of parallels with and without a common perpendicular. This part also deals with horocycles and triangle relations. The third part examines single and double elliptic geometries. This book will be of great value to mathematics, liberal arts, and philosophy major students.

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209294

Get Book

Geometry of Surfaces by John Stillwell Pdf

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 no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.

Author : Michael P. Hitchman
Publisher : Jones & Bartlett Learning
Page : 255 pages
File Size : 40,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780763754570

Get Book

Geometry with an Introduction to Cosmic Topology by Michael P. Hitchman Pdf

The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 46,9 Mb
Release : 2005-08-09
Category : Mathematics
ISBN : 9780387255309

Get Book

The Four Pillars of Geometry by John Stillwell Pdf

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 algebraic Abundantly supplemented with figures and exercises

Author : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 237 pages
File Size : 47,7 Mb
Release : 2009-09-04
Category : Mathematics
ISBN : 9780521127073

Get Book

Euclidean and Non-Euclidean Geometry International Student Edition by Patrick J. Ryan Pdf

This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.

Author : I.M. Yaglom
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261353

Get Book

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.

Author : Henry Parker Manning
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 1963
Category : Geometry
ISBN : LCCN:63003592

Get Book

Introductory Non-Euclidean Geometry by Henry Parker Manning Pdf

Author : András Prékopa,Emil Molnár
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 49,6 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9780387295558

Get Book

Non-Euclidean Geometries by András Prékopa,Emil Molnár Pdf

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

Author : Arlan Ramsay,Robert D. Richtmyer
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 48,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475755855

Get Book

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.

Author : Jacques Hadamard
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 44,6 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821890476

Get Book

Non-Euclidean Geometry in the Theory of Automorphic Functions by Jacques Hadamard Pdf

This is the English translation of a volume originally published only in Russian and now out of print. The book was written by Jacques Hadamard on the work of Poincare. Poincare's creation of a theory of automorphic functions in the early 1880s was one of the most significant mathematical achievements of the nineteenth century. It directly inspired the uniformization theorem, led to a class of functions adequate to solve all linear ordinary differential equations, and focused attention on a large new class of discrete groups. It was the first significant application of non-Euclidean geometry. This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts.

Author : H. S. M. Coxeter
Publisher : Cambridge University Press
Page : 362 pages
File Size : 54,5 Mb
Release : 1998-09-17
Category : Mathematics
ISBN : 0883855224

Get Book

Non-Euclidean Geometry by H. S. M. Coxeter Pdf

A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.

Author : Marvin J. Greenberg
Publisher : Macmillan
Page : 512 pages
File Size : 43,7 Mb
Release : 1993-07-15
Category : Mathematics
ISBN : 0716724464

Get Book

Euclidean and Non-Euclidean Geometries by Marvin J. Greenberg Pdf

This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.