Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
The Real Projective Plane
.
Bookmark this Record
Catalogue Record 44811
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 44811
.
Reviews
Catalogue Record 44811
.
British Library
Resolver for RSN-44811
Google Scholar
Resolver for RSN-44811
WorldCat
Resolver for RSN-44811
Catalogo Nazionale SBN
Resolver for RSN-44811
GoogleBooks
Resolver for RSN-44811
ICTP Library
Resolver for RSN-44811
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
516
Title
The Real Projective Plane ([EBook]) / by H. S. M. Coxeter, George Beck.
Author
Coxeter, Harold Scott Macdonald , 1907-2003
Added Personal Name
Beck, George
Other name(s)
SpringerLink (Online service)
Edition statement
Third Edition.
Publication
New York, NY : Springer , 1993.
Physical Details
XIV, 227 p. : online resource.
ISBN
9781461227342
Summary Note
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.:
Contents note
1. A Comparison of Various Kinds of Geometry -- 1·1 Introduction -- 1·2 Parallel projection -- 1·3 Central projection -- 1·4 The line at infinity -- 1·5 Desargues’s two-triangle theorem -- 1·6 The directed angle, or cross -- 1·7 Hexagramma mysticum -- 1·8 An outline of subsequent work -- 2. Incidence -- 1·1 Primitive concepts -- 2·2 The axioms of incidence -- 2·3 The principle of duality -- 2·4 Quadrangle and quadrilateral -- 2·5 Harmonic conjugacy -- 2·6 Ranges and pencils -- 2·7 Perspectivity -- 2·8 The invariance and symmetry of the harmonic relation -- 3. Order and Continuity -- 3·1 The axioms of order -- 3·2 Segment and interval -- 3·3 Sense -- 3·4 Ordered correspondence -- 3·5 Continuity -- 3·6 Invariant points -- 3·7 Order in a pencil -- 3·8 The four regions determined by a triangle -- 4. One-Dimensional Projectivities -- 4·1 Projectivity -- 4·2 The fundamental theorem of projective geometry -- 4·3 Pappus’s theorem -- 4·4 Classification of projectivities -- 4·5 Periodic projectivities -- 4·6 Involution -- 4·7 Quadrangular set of six points -- 4·8 Projective pencils -- 5. Two-Dimensional Projectivities -- 5·1 Collineation -- 5·2 Perspective collineation -- 5·3 Involutory collineation -- 5·4 Correlation -- 5·5 Polarity -- 5·6 Polar and self-polar triangles -- 5·7 The self-polarity of the Desargues configuration -- 5·8 Pencil and range of polarities -- 5·9 Degenerate polarities -- 6. Conics -- 6·1 Historial remarks -- 6·2 Elliptic and hyperbolic polarities -- 6·3 How a hyperbolic polarity determines a conic -- 6·4 Conjugate points and conjugate lines -- 6·5 Two possible definitions for a conic -- 6·6 Construction for the conic through five given points -- 6·7 Two triangles inscribed in a conic -- 6·8 Pencils of conics -- 7. Projectivities on a Conic -- 7·1 Generalized perspectivity -- 7·2 Pascal and Brianchon -- 7·3 Construction for a projectivity on a conic -- 7·4 Construction for the invariant points of a given hyperbolic projectivity -- 7·5 Involution on a conic -- 7·6 A generalization of Steiner’s construction -- 7·7 Trilinear polarity -- 8. Affine Geometry -- 8·1 Parallelism -- 8·2 Intermediacy -- 8·3 Congruence -- 8·4 Distance -- 8·5 Translation and dilatation -- 8·6 Area -- 8·7 Classification of conics -- 8·8 Conjugate diameters -- 8·9 Asymptotes -- 8·10 Affine transformations and the Erlangen programme -- 9. Euclidean Geometry -- 9·1 Perpendicularity -- 9·2 Circles -- 9·3 Axes of a conic -- 9·4 Congruent segments -- 9·5 Congruent angles -- 9·6 Congruent transformations -- 9·7 Foci -- 9·8 Directrices -- 10. Continuity -- 10·1 An improved axiom of continuity -- 10·2 Proving Archimedes’ axiom -- 10·3 Proving the line to be perfect -- 10·4 The fundamental theorem of projective geometry -- 10·5 Proving Dedekind’s axiom -- 10·6 Enriques’s theorem -- 11. The Introduction of Coordinates -- 11·1 Addition of points -- 11·2 Multiplication of points -- 11·3 Rational points -- 11·4 Projectivities -- 11·5 The one-dimensional continuum -- 11·6 Homogeneous coordinates -- 11·7 Proof that a line has a linear equation -- 11·8 Line coordinates -- 12. The Use of Coordinates -- 12·1 Consistency and categoricalness -- 12·2 Analytic geometry -- 12·3 Verifying the axioms of incidence -- 12·4 Verifying the axioms of order and continuity -- 12·5 The general collineation -- 12·6 The general polarity -- 12·7 Conies -- 12·8 The affine plane: affine and areal coordinates -- 12·9 The Euclidean plane: Cartesian and trilinear coordinates.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4612-2734-2
Links to Related Works
Subject References:
Geometry
.
Mathematics
.
Authors:
author
.
Beck, George
.
Coxeter, Harold Scott Macdonald 1907-2003
.
Coxeter, Harold Scott Macdonald, 1907-2003.
.
Corporate Authors:
SpringerLink (Online service)
.
Classification:
516
.
.
ISBD Display
Catalogue Record 44811
.
Tag Display
Catalogue Record 44811
.
Related Works
Catalogue Record 44811
.
Marc XML
Catalogue Record 44811
.
Add Title to Basket
Catalogue Record 44811
.
Catalogue Information 44811
Beginning of record
.
Catalogue Information 44811
Top of page
.
Download Title
Catalogue Record 44811
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
44811
1
44811
-
2
44811
-
3
44811
-
4
44811
-
5
44811
-
Quick Search
Search for