Euclidean and Non-Euclidean Geometries PDF Download
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Author: Marvin J. Greenberg
Publisher: Macmillan
ISBN: 9780716724469
Category : Mathematics
Languages : en
Pages : 512
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Book Description
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.
Author: Marvin J. Greenberg
Publisher: Macmillan
ISBN: 9780716724469
Category : Mathematics
Languages : en
Pages : 512
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Book Description
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.
Author: Maria Helena Noronha
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 440
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Book Description
This book develops a self-contained treatment of classical Euclidean geometry through both axiomatic and analytic methods. Concise and well organized, it prompts readers to prove a theorem yet provides them with a framework for doing so. Chapter topics cover neutral geometry, Euclidean plane geometry, geometric transformations, Euclidean 3-space, Euclidean n-space; perimeter, area and volume; spherical geometry; hyperbolic geometry; models for plane geometries; and the hyperbolic metric.
Author: Boris A. Rosenfeld
Publisher: Springer Science & Business Media
ISBN: 1441986804
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: Patrick J. Ryan
Publisher: Cambridge University Press
ISBN: 0521127076
Category : Mathematics
Languages : en
Pages : 237
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Book Description
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Author: Henry Parker Manning
Publisher: Courier Corporation
ISBN: 0486154645
Category : Mathematics
Languages : en
Pages : 110
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Book Description
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.
Author: András Prékopa
Publisher: Springer Science & Business Media
ISBN: 0387295550
Category : Mathematics
Languages : en
Pages : 497
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Book Description
"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.
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 1461209293
Category : Mathematics
Languages : en
Pages : 225
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Book Description
The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Author: Harold E. Wolfe
Publisher: Courier Corporation
ISBN: 0486498506
Category : Mathematics
Languages : en
Pages : 274
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Book Description
One of the first college-level texts for elementary courses in non-Euclidean geometry, this volumeis geared toward students familiar with calculus. Topics include the fifth postulate, hyperbolicplane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensiveappendixes offer background information on Euclidean geometry, and numerous exercisesappear throughout the text.Reprint of the Holt, Rinehart & Winston, Inc., New York, 1945 edition
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 0387255303
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Author: Michael Henle
Publisher: Pearson
ISBN:
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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.
