A history of non-euclidean geometry : evolution of the concept of a geometric space
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Bibliographic Information
A history of non-euclidean geometry : evolution of the concept of a geometric space
（Studies in the history of mathematics and physical sciences, 12）
Springer-Verlag, c1988
- : us
- : gw
- Other Title
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Istorii︠a︡ neevklidovoĭ geometrii
History of noneuclidean geometry
Available at / 51 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: usROS||48||1(S)88061949
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:516/R8172070181784
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Note
Translation of: Istorii︠a︡ neevklidovoĭ geometrii
Bibliography: p. [428]-454
Includes index
Description and Table of Contents
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.
Table of Contents
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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