Introductory Non Euclidean Geometry

Author: Henry Parker Manning
Publisher: Courier Corporation
ISBN: 9780486154640
Release Date: 2013-01-30
Genre: Mathematics

This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.

Introduction to Non Euclidean Geometry

Author: Harold E. Wolfe
Publisher: Courier Corporation
ISBN: 9780486320373
Release Date: 2013-09-26
Genre: Mathematics

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.

Non Euclidean Geometry

Author: H. S. M. Coxeter
Publisher: Cambridge University Press
ISBN: 0883855224
Release Date: 1998-09-17
Genre: Mathematics

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.

Introduction to Non Euclidean Geometry

Author: EISENREICH
Publisher: Elsevier
ISBN: 9781483295312
Release Date: 2014-06-28
Genre: Mathematics

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.

Taxicab Geometry

Author: Eugene F. Krause
Publisher: Courier Corporation
ISBN: 9780486136066
Release Date: 2012-04-30
Genre: Mathematics

Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.

Introduction to Hyperbolic Geometry

Author: Arlan Ramsay
Publisher: Springer Science & Business Media
ISBN: 9781475755855
Release Date: 2013-03-09
Genre: Mathematics

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.

Advanced Euclidean Geometry

Author: Roger A. Johnson
Publisher: Dover Publications
ISBN: CORNELL:31924107164471
Release Date: 2007-08-31
Genre: Mathematics

For many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry.

Introduction to Projective Geometry

Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 9780486141701
Release Date: 2011-09-12
Genre: Mathematics

This introductory volume offers strong reinforcement for its teachings, with detailed examples and numerous theorems, proofs, and exercises, plus complete answers to all odd-numbered end-of-chapter problems. 1970 edition.

Geometry of Complex Numbers

Author: Hans Schwerdtfeger
Publisher: Courier Corporation
ISBN: 9780486135861
Release Date: 2012-05-23
Genre: Mathematics

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

College Geometry

Author: Nathan Altshiller-Court
Publisher: Courier Corporation
ISBN: 9780486141374
Release Date: 2012-06-29
Genre: Mathematics

The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Euclidean Geometry and Transformations

Author: Clayton W. Dodge
Publisher: Courier Corporation
ISBN: 9780486138428
Release Date: 2012-04-26
Genre: Mathematics

This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.

Problems and Solutions in Euclidean Geometry

Author: M. N. Aref
Publisher: Courier Corporation
ISBN: 9780486477206
Release Date: 2010
Genre: Mathematics

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.

Lectures on Hyperbolic Geometry

Author: Riccardo Benedetti
Publisher: Springer Science & Business Media
ISBN: 9783642581588
Release Date: 2012-12-06
Genre: Mathematics

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.

Geometry Euclid and Beyond

Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 9780387226767
Release Date: 2013-11-11
Genre: Mathematics

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Geometry A Comprehensive Course

Author: Dan Pedoe
Publisher: Courier Corporation
ISBN: 9780486131733
Release Date: 2013-04-02
Genre: Mathematics

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.