A history of non-euclidean geometry : evolution of the concept of a geometric space

B.A. Rosenfeld ; translated by Abe Schenitzer ; with the editorial assistance of Hardy Grant

This book is an investigation of the mathematical and philosophical factors underlying the discovery of the concept of noneuclidean geometries, and the subsequent extension of the concept of space. Chapters one through five are devoted to the evolution of the concept of space, leading up to chapter six which describes the discovery of noneuclidean geometry, and the corresponding broadening of the concept of space. The author goes on to discuss concepts such as multidimensional spaces and curvature, and transformation groups. The book ends with a chapter describing the applications of nonassociative algebras to geometry.

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  • 1. Spherical Geometry.- 2. The Theory of Parallels.- 3. Geometric Transformations.- 4. Geometric Algebra and the Prehistory of Multidimensional Geometry.- 5. Philosophy of Space.- 6. Lobacevskian Geometry.- 7. Multidimensional Spaces.- 8. The Curvature of Space.- 9. Groups of Transformations.- 10. Application of Algebras.- References.

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書名 A history of non-euclidean geometry : evolution of the concept of a geometric space
著作者等 Rozenfelʹd, B. A.
Grant Hardy
Shenitzer Abe
Rosenfeld B. A.
書名別名 History of noneuclidean geometry

Istorii︠a︡ neevklidovoĭ geometrii
シリーズ名 Studies in the history of mathematics and physical sciences
出版元 Springer-Verlag
刊行年月 c1988
ページ数 ix, 471 p.
大きさ 24 cm
ISBN 3540964584
NCID BA04519914
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言語 英語
原文言語 ロシア語
出版国 アメリカ合衆国