Introductory Non-Euclidean Geometry

Author: Henry Parker Manning

Publisher: Courier Corporation

ISBN: 0486154645

Category: Mathematics

Page: 112

View: 9075

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: 0486320375

Category: Mathematics

Page: 272

View: 6888

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: 9780883855225

Category: Mathematics

Page: 336

View: 7901

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.

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 1094

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 Projective Geometry

Author: C. R. Wylie

Publisher: Courier Corporation

ISBN: 0486141705

Category: Mathematics

Page: 576

View: 3246

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.

Introduction to Hyperbolic Geometry

Author: Arlan Ramsay,Robert D. Richtmyer

Publisher: Springer Science & Business Media

ISBN: 1475755856

Category: Mathematics

Page: 289

View: 1510

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: Courier Corporation

ISBN: 048615498X

Category: Mathematics

Page: 336

View: 4931

This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.

Geometry of Complex Numbers

Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 2368

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

Lectures on Hyperbolic Geometry

Author: Riccardo Benedetti,Carlo Petronio

Publisher: Springer Science & Business Media

ISBN: 3642581587

Category: Mathematics

Page: 330

View: 7883

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.

College Geometry

An Introduction to the Modern Geometry of the Triangle and the Circle

Author: Nathan Altshiller-Court

Publisher: Courier Corporation

ISBN: 0486141373

Category: Mathematics

Page: 336

View: 9575

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.

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 5760

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.

Euclidean Geometry and Transformations

Author: Clayton W. Dodge

Publisher: Courier Corporation

ISBN: 0486138429

Category: Mathematics

Page: 304

View: 1510

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,William Wernick

Publisher: Courier Corporation

ISBN: 0486477207

Category: Mathematics

Page: 258

View: 4859

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.

Hyperbolic Geometry

Author: James W. Anderson

Publisher: Springer Science & Business Media

ISBN: 1447139879

Category: Mathematics

Page: 230

View: 3358

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

Geometry of Lengths, Areas, and Volumes: Two-Dimensional Spaces, Volume 1

Author: James W. Cannon

Publisher: American Mathematical Soc.

ISBN: 1470437147

Category: Geometry

Page: 119

View: 9933

This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of and , of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.

Non-Euclidean Geometry

A Critical and Historical Study of Its Development

Author: Roberto Bonola

Publisher: Courier Dover Publications


Category: Mathematics

Page: 389

View: 7932

Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs, and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.

Foundations of Geometry

Author: C. R. Wylie

Publisher: Courier Corporation

ISBN: 0486472140

Category: Education

Page: 338

View: 6587

Explains geometric theories and shows many examples.

Geometry, Relativity and the Fourth Dimension

Author: Rudolf Rucker

Publisher: Courier Corporation

ISBN: 0486140334

Category: Science

Page: 160

View: 8243

Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

Foundations and Fundamental Concepts of Mathematics

Author: Howard Eves

Publisher: Courier Corporation

ISBN: 048613220X

Category: Mathematics

Page: 368

View: 2996

Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.