Non Euclidean Geometries
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Non Euclidean Geometry Sixth Edition
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Author : H. S. M. Coxeter
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-12-31
Non Euclidean Geometry Sixth Edition written by H. S. M. Coxeter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Mathematics categories.
A reissue of Professor Coxeter's classic text on non-euclidean geometry.
Non Euclidean Geometry
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Author : Roberto Bonola
language : en
Publisher: Courier Corporation
Release Date : 2012-08-15
Non Euclidean Geometry written by Roberto Bonola and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-15 with Mathematics categories.
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.
A History Of Non Euclidean Geometry
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Author : Boris A. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-08
A History Of Non Euclidean Geometry written by Boris A. Rosenfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-08 with Mathematics categories.
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.
Introduction To Non Euclidean Geometry
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Author : Harold E. Wolfe
language : en
Publisher: Courier Corporation
Release Date : 2013-09-26
Introduction To Non Euclidean Geometry written by Harold E. Wolfe and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
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.
The Elements Of Non Euclidean Geometry
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Author : Julian Lowell Coolidge, PhD
language : en
Publisher:
Release Date : 2020-06-04
The Elements Of Non Euclidean Geometry written by Julian Lowell Coolidge, PhD and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-04 with categories.
In this book Dr. Coolidge explains non-Euclidean geometry which consists of two geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is replaced with an alternative one. In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry. The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any line through A intersects l. Another way to describe the differences between these geometries is to consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line: In Euclidean geometry, the lines remain at a constant distance from each other (meaning that a line drawn perpendicular to one line at any point will intersect the other line and the length of the line segment joining the points of intersection remains constant) and are known as parallels. In hyperbolic geometry, they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels. In elliptic geometry, the lines "curve toward" each other and intersect.
Euclidean And Non Euclidean Geometries
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Author : Marvin J. Greenberg
language : en
Publisher: WH Freeman
Release Date : 2007-09-28
Euclidean And Non Euclidean Geometries written by Marvin J. Greenberg and has been published by WH Freeman this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-28 with Mathematics categories.
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.
Introduction To Non Euclidean Geometry
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Author : EISENREICH
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Introduction To Non Euclidean Geometry written by EISENREICH and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
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.
A Simple Non Euclidean Geometry And Its Physical Basis
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Author : I.M. Yaglom
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Simple Non Euclidean Geometry And Its Physical Basis written by I.M. Yaglom and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Elements Of Non Euclidean Geometry
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Author : D. M.Y. Sommerville
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
The Elements Of Non Euclidean Geometry written by D. M.Y. Sommerville and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
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.
Non Euclidean Geometry
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Author : Harold Scott Macdonald Coxeter
language : en
Publisher:
Release Date : 1947
Non Euclidean Geometry written by Harold Scott Macdonald Coxeter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with Geometry, Non-Euclidean categories.