Non-Euclidean Geometry


Author: H. S. M. Coxeter
Publisher: Cambridge University Press
ISBN: 9780883855225
Category: Mathematics
Page: 336
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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.

The Elements of Non-Euclidean Geometry


Author: D. M.Y. Sommerville
Publisher: Courier Corporation
ISBN: 0486154580
Category: Mathematics
Page: 288
View: 2727

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Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.

Introduction to Non-Euclidean Geometry


Author: Harold E. Wolfe
Publisher: Courier Corporation
ISBN: 0486320375
Category: Mathematics
Page: 272
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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.

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: 3904

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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.

Non-Euclidean Geometry


Author: Roberto Bonola
Publisher: Cosimo, Inc.
ISBN: 1602064652
Category: Mathematics
Page: 288
View: 2409

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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.

Non-Euclidean Geometry


Author: Stefan Kulczycki
Publisher: Courier Corporation
ISBN: 0486155013
Category: Mathematics
Page: 208
View: 1534

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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.

Introduction to Non-Euclidean Geometry


Author: EISENREICH
Publisher: Elsevier
ISBN: 1483295311
Category: Mathematics
Page: 274
View: 8418

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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.

Introductory Non-Euclidean Geometry


Author: Henry Parker Manning
Publisher: Courier Corporation
ISBN: 0486154645
Category: Mathematics
Page: 112
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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.

Non-Euclidean Geometries

János Bolyai Memorial Volume
Author: András Prékopa,Emil Molnár
Publisher: Springer Science & Business Media
ISBN: 0387295550
Category: Mathematics
Page: 506
View: 7292

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"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.

Non-Euclidean Geometry in the Theory of Automorphic Functions


Author: Jacques Hadamard
Publisher: American Mathematical Soc.
ISBN: 9780821890479
Category: Mathematics
Page: 95
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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.

The Foundations of Geometry and the Non-Euclidean Plane


Author: G.E. Martin
Publisher: Springer Science & Business Media
ISBN: 9780387906942
Category: Mathematics
Page: 512
View: 3299

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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.

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: 7958

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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.

Euclidean and Non-Euclidean Geometries

Development and History
Author: Marvin J. Greenberg
Publisher: Macmillan Higher Education
ISBN: 1429281332
Category: Mathematics
Page: 512
View: 8194

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This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.

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


Author: Jeremy Gray,Professor of History of Mathematics Jeremy J Gray,János Bolyai
Publisher: MIT Press
ISBN: 9780262571746
Category: Mathematics
Page: 239
View: 9531

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An account of the major work of Janos Bolyai, a nineteenth-century mathematician who set the stage for the field of non-Euclidean geometry. Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twenty-four-page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry. Bolyai's "Appendix" (published as just that--an appendix to a much longer mathematical work by his father) set up a series of mathematical proposals whose implications would blossom into the new field of non-Euclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp. In this short book, Jeremy Gray explains Bolyai's ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition. Intended for nonspecialists, the book includes facsimiles of Bolyai's original paper and the 1898 English translation by G. B. Halstead, both reproduced from copies in the Burndy Library at MIT.

Taxicab Geometry

An Adventure in Non-Euclidean Geometry
Author: Eugene F. Krause
Publisher: Courier Corporation
ISBN: 048613606X
Category: Mathematics
Page: 96
View: 8488

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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.

Bibliography of Non-Euclidean Geometry

Including the Theory of Parallels, the Foundation of Geometry, and Space of N Dimensions
Author: Duncan M'Laren Young Sommerville,University of St. Andrews
Publisher: N.A
ISBN: N.A
Category: Geometry, Non-Euclidean
Page: 403
View: 5742

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