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.
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Non-Euclidean Geometry

Author: Roberto Bonola

Publisher: Courier Corporation

ISBN: 048615503X

Category: Mathematics

Page: 448

View: 2986

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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.
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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: 3165

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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.
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Introduction to Non-Euclidean Geometry

Author: EISENREICH

Publisher: Elsevier

ISBN: 1483295311

Category: Mathematics

Page: 274

View: 5568

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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.
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Euclidean and Non-Euclidean Geometries

Development and History

Author: Marvin J. Greenberg

Publisher: Macmillan

ISBN: 1429281332

Category: Mathematics

Page: 512

View: 8392

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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.
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Non-Euclidean Geometry

Hyperbolic Geometry, Hyperbolic Function, Gyrovector Space, Parallel Postulate, Sl2(R), Apollonian Gasket, Split-Quaternion, T

Author: Source Wikipedia

Publisher: University-Press.org

ISBN: 9781230579559

Category:

Page: 72

View: 6374

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 71. Chapters: Hyperbolic geometry, Hyperbolic function, Gyrovector space, Parallel postulate, SL2(R), Apollonian gasket, Split-quaternion, Triangle group, Poincare half-plane model, Elliptic geometry, Fuchsian group, Hyperbolic space, Hyperbolic angle, Poincare metric, Hyperboloid model, Hilbert's theorem, Anosov diffeomorphism, Hyperbolization theorem, Schwarz lemma, Hilbert's arithmetic of ends, Hyperbolic coordinates, Beltrami-Klein model, Rips machine, Poincare disk model, Mostow rigidity theorem, (2,3,7) triangle group, Hyperbolic motion, Pair of pants, Hypercycle, Schopenhauer's criticism of the proofs of the parallel postulate, Hyperbolic triangle, Uniform tilings in hyperbolic plane, Hyperbolic tree, Angle of parallelism, Tameness theorem, Ultraparallel theorem, Dehn planes, Hyperbolic 3-manifold, Macbeath surface, Saccheri quadrilateral, Ending lamination theorem, Caratheodory metric, Hjelmslev transformation, Weeks manifold, Picard horn, Hyperbolic Dehn surgery, Schoen-Yau conjecture, Geometric finiteness, Ideal triangle, Earthquake map, Bolza surface, Fuchsian model, The geometry and topology of three-manifolds, Upper half-plane, Double limit theorem, Complex geodesic, Hyperbolic manifold, Geometric topology, Hyperbolic law of cosines, Cusp neighborhood, Gieseking manifold, Arithmetic hyperbolic 3-manifold, Meyerhoff manifold, Non-positive curvature, Horocycle, Pleated surface, Tame manifold, Schwarz-Ahlfors-Pick theorem, Margulis lemma, Non-Euclidean crystallographic group, Apollonian sphere packing, Lambert quadrilateral, Hyperbolic volume, Saccheri-Legendre theorem, Horoball, Kleinian model, Bryant surface.
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Modern Geometries

Non-Euclidean, Projective, and Discrete

Author: Michael Henle

Publisher: Pearson College Division

ISBN: 9780130323132

Category: Mathematics

Page: 389

View: 936

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Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.
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