The Real Projective Plane
Title | The Real Projective Plane PDF eBook |
Author | H.S.M. Coxeter |
Publisher | Springer Science & Business Media |
Total Pages | 236 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461227348 |
Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
The Real Projective Plane
Title | The Real Projective Plane PDF eBook |
Author | H.S.M. Coxeter |
Publisher | Springer Science & Business Media |
Total Pages | 248 |
Release | 1992-12-23 |
Genre | Mathematics |
ISBN | 9780387978895 |
Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
The Real Projective Plane
Title | The Real Projective Plane PDF eBook |
Author | Harold Scott Macdonald Coxeter |
Publisher | |
Total Pages | 226 |
Release | 1961 |
Genre | |
ISBN |
Mathematical models
Title | Mathematical models PDF eBook |
Author | Gerd Fischer |
Publisher | Informatica International, Incorporated |
Total Pages | 118 |
Release | 1986 |
Genre | Mathematics |
ISBN |
The Real Projective Plane
Title | The Real Projective Plane PDF eBook |
Author | H. S. M. Coxeter |
Publisher | |
Total Pages | 0 |
Release | 2003 |
Genre | Mathematics |
ISBN | 9780758111661 |
Perspectives on Projective Geometry
Title | Perspectives on Projective Geometry PDF eBook |
Author | Jürgen Richter-Gebert |
Publisher | Springer Science & Business Media |
Total Pages | 573 |
Release | 2011-02-04 |
Genre | Mathematics |
ISBN | 3642172865 |
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
The Real Projective Plane
Title | The Real Projective Plane PDF eBook |
Author | Harold S. M. Coxeter |
Publisher | |
Total Pages | 222 |
Release | 1993-01-01 |
Genre | Geometry, Projective |
ISBN | 9783540978893 |
Contain: Files, scenes, narrations, and projectivities for Mathematica.