The Real Projective Plane

H S M Coxeter

ISBN 10: 0387978895 / ISBN 13: 9780387978895

Edité par Springer New York, 1992

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9780387978895

Détails bibliographiques

• Titre: The Real Projective Plane
• Éditeur: Springer New York
• Date de parution: 1992
• Langue: anglais
• ISBN à 10 chiffres: 0387978895
• ISBN à 13 chiffres: 9780387978895
• Reliure: Taschenbuch
• Édition: 3ème Édition
• État de l'article: Neu
• Dimensions: 240 L x 161 H x 19 P (en millimètres) 240 millimètres de largeur par 161 millimètres de hauteur par 19 millimètres de profondeur
• Poids: 531 grammes

A propos de ce titre

Synopsis

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.