Non-Euclidean Geometry

Author: H. S. M. Coxeter

Publisher: Cambridge University Press

ISBN: 9780883855225

Category: Mathematics

Page: 336

View: 6885

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.

Introductory Non-Euclidean Geometry

Author: Henry Parker Manning

Publisher: Courier Corporation

ISBN: 0486154645

Category: Mathematics

Page: 112

View: 2334

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


Publisher: Elsevier

ISBN: 1483295311

Category: Mathematics

Page: 274

View: 714

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.

Euclidean and Non-Euclidean Geometry International Student Edition

An Analytic Approach

Author: Patrick J. Ryan

Publisher: Cambridge University Press

ISBN: 0521127076

Category: Mathematics

Page: 232

View: 8439

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

A History of Non-Euclidean Geometry

Evolution of the Concept of a Geometric Space

Author: Boris A. Rosenfeld

Publisher: Springer Science & Business Media

ISBN: 1441986804

Category: Mathematics

Page: 471

View: 2410

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.

Euclidean and Non-euclidean Geometries

Author: Maria Helena Noronha

Publisher: N.A


Category: Mathematics

Page: 409

View: 7743

Designed for undergraduate juniors and seniors, Noronha's (California State U., Northridge) clear, no-nonsense text provides a complete treatment of classical Euclidean geometry using axiomatic and analytic methods, with detailed proofs provided throughout. Non-Euclidean geometries are presented usi

Non-Euclidean Geometry

A Critical and Historical Study of Its Development

Author: Roberto Bonola

Publisher: Courier Dover Publications


Category: Mathematics

Page: 389

View: 9966

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.

Introduction to Non-Euclidean Geometry

Author: Harold E. Wolfe

Publisher: Courier Corporation

ISBN: 0486320375

Category: Mathematics

Page: 272

View: 502

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 Geometries

János Bolyai Memorial Volume

Author: András Prékopa,Emil Molnár

Publisher: Springer Science & Business Media

ISBN: 0387295550

Category: Mathematics

Page: 506

View: 5636

"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.

Elements of Non-Euclidean Geometry ...

Author: Duncan M'Laren Young Sommerville

Publisher: N.A


Category: Geometry, Non-Euclidean

Page: 274

View: 5268

Euclidean and Non-Euclidean Geometries

Development and History

Author: Marvin J. Greenberg

Publisher: Macmillan

ISBN: 9780716724469

Category: Mathematics

Page: 483

View: 416

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.

A Simple Non-Euclidean Geometry and Its Physical Basis

An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity

Author: I.M. Yaglom

Publisher: Springer Science & Business Media

ISBN: 146126135X

Category: Mathematics

Page: 307

View: 4836

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.

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 5931

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.

A New Perspective on Relativity

An Odyssey in Non-Euclidean Geometries

Author: Bernard H. Lavenda

Publisher: World Scientific

ISBN: 9814340480

Category: Science

Page: 668

View: 8281

Starting off from noneuclidean geometries, apart from the method of Einstein's equations, this book derives and describes the phenomena of gravitation and diffraction. A historical account is presented, exposing the missing link in Einstein's construction of the theory of general relativity: the uniformly rotating disc, together with his failure to realize, that the Beltrami metric of hyperbolic geometry with constant curvature describes exactly the uniform acceleration observed. This book also explores these questions: * How does time bend? * Why should gravity propagate at the speed of light? * How does the expansion function of the universe relate to the absolute constant of the noneuclidean geometries? * Why was the Sagnac effect ignored? * Can Maxwell's equations accommodate mass? * Is there an inertia due solely to polarization? * Can objects expand in elliptic geometry like they contract in hyperbolic geometry?

Non-Euclidean Geometry

Author: Stefan Kulczycki

Publisher: Courier Corporation

ISBN: 0486155013

Category: Mathematics

Page: 208

View: 3330

This accessible approach features stereometric and planimetric proofs, and elementary proofs employing only the simplest properties of the plane. A short history of geometry precedes the systematic exposition. 1961 edition.

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: 4137

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.

The Foundations of Geometry and the Non-Euclidean Plane

Author: G.E. Martin

Publisher: Springer Science & Business Media

ISBN: 1461257255

Category: Mathematics

Page: 512

View: 7846

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.

The Non-Euclidean Revolution

With an Introduction by H.S.M Coxeter

Author: Richard J. Trudeau

Publisher: Springer Science & Business Media

ISBN: 1461221021

Category: Mathematics

Page: 270

View: 2797

Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world.

János Bolyai, Non-Euclidean Geometry, and the Nature of Space

Author: Jeremy Gray

Publisher: MIT Press

ISBN: 9780262571746

Category: Mathematics

Page: 239

View: 8813

An account of the major work of Janos Bolyai, a nineteenth-century mathematician who set the stage for the field of non-Euclidean geometry.

Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein

Author: L. Redei

Publisher: Elsevier

ISBN: 1483282708

Category: Mathematics

Page: 410

View: 3381

Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein aims to remedy the deficiency in geometry so that the ideas of F. Klein obtain the place they merit in the literature of mathematics. This book discusses the axioms of betweenness, lattice of linear subspaces, generalization of the notion of space, and coplanar Desargues configurations. The central collineations of the plane, fundamental theorem of projective geometry, and lines perpendicular to a proper plane are also elaborated. This text likewise covers the axioms of motion, basic projective configurations, properties of triangles, and theorem of duality in projective space. Other topics include the point-coordinates in an affine space and consistency of the three geometries. This publication is beneficial to mathematicians and students learning geometry.