The Real Projective Plane PDF Download
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Author: H.S.M. Coxeter
Publisher: Springer Science & Business Media
ISBN: 1461227348
Category : Mathematics
Languages : en
Pages : 236
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Book Description
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.
Author: H.S.M. Coxeter
Publisher: Springer Science & Business Media
ISBN: 1461227348
Category : Mathematics
Languages : en
Pages : 236
Get Book
Book Description
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.
Author: H.S.M. Coxeter
Publisher: Springer Science & Business Media
ISBN: 9780387978895
Category : Mathematics
Languages : en
Pages : 248
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Book Description
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.
Author: Harold Scott Macdonald Coxeter
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 226
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Book Description
Author: Abraham Adrian Albert
Publisher: Courier Corporation
ISBN: 0486789942
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Text for both beginning and advanced undergraduate and graduate students covers finite planes, field planes, coordinates in an arbitrary plane, central collineations and the little Desargues' property, the fundamental theorem, and non-Desarguesian planes. 1968 edition.
Author: H. S. M. Coxeter
Publisher:
ISBN: 9780758111661
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Author: Gerd Fischer
Publisher: Informatica International, Incorporated
ISBN:
Category : Mathematics
Languages : en
Pages : 118
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Book Description
Author: Harold S. M. Coxeter
Publisher:
ISBN: 9783540978893
Category : Geometry, Projective
Languages : en
Pages : 222
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Book Description
Contain: Files, scenes, narrations, and projectivities for Mathematica.
Author: Séverine Fiedler - Le Touzé
Publisher: Chapman & Hall/CRC
ISBN: 9781138322578
Category : Curves, Algebraic
Languages : en
Pages : 0
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Book Description
Part 1 of this book answers questions for using rational cubics and pencils of cubics. Part 2 deals with configurations of eight points in convex position. Part 3 contains applications and results around Hilbert's sixteenth problem.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 226
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Book Description
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 3642172865
Category : Mathematics
Languages : en
Pages : 571
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Book Description
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.
