Açıklama
The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section 15.9 on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Transformations that preserve incidence are called colineations. They lead in a natural way to elliptic isometries or "congruent transformations". Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory. - Publisher.
Baskılar ve ISBN
- 2019
- University of Toronto Press · İngilizce
ISBN 9781442653207 - Dec 15, 1965
- University of Toronto Press, Scholarly Publishing · 326 sayfa
ISBN 9781442639454 - 1998
- Mathematical Association of America · İngilizce · 336 sayfa
ISBN 0883855224 - June 1965
- Univ of Toronto Pr · İngilizce · 326 sayfa
ISBN 9780802010681
Künye
- Yazar
- H. S. M. Coxeter
- İlk yayın
- 1942
- Yayınevleri
- The University of Toronto press, Mathematical Association of America, Toronto U.P.; Oxford U.P, University of Toronto Press, Scholarly Publishing, The Unviversity of Toronto press
- Sayfa (ortalama)
- 309
- Baskı sayısı
- 31
- Kaynak
- Open Library