The real projective plane: PC version (Diskette provided)
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest
Springer
1993
|
| Ausgabe: | Third edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 222 Seiten Illustrationen, Diagramme 1 Diskette, 5,25" |
| ISBN: | 0387978895 3540978895 |
Internformat
MARC
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| 100 | 1 | |a Coxeter, Harold S. M. |d 1907-2003 |e Verfasser |0 (DE-588)118522507 |4 aut | |
| 245 | 1 | 0 | |a The real projective plane |b PC version (Diskette provided) |c H. S. M. Coxeter. With an appendix for Mathematica by George Beck |
| 250 | |a Third edition | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest |b Springer |c 1993 | |
| 264 | 4 | |c © 1993 | |
| 300 | |a xiii, 222 Seiten |b Illustrationen, Diagramme |e 1 Diskette, 5,25" | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804122523312324608 |
|---|---|
| adam_text | Contents
Preface to the Third Edition page v
Preface to the Second Edition vii
Preface to the First Edition ix
Chapter 1. a comparison of various kinds of geometry
1 1 Introduction, p. 1. 1 2 Parallel projection, p. 1. 1 3 Central projection, p. 2.
T4 The line at infinity, p. 4. 1 5 Desargues s two triangle theorem, p. 6. 1 6 The
directed angle, or cross, p. 8. 1 7 Hexagramma mysticum, p. 9. 1 8 An outline of
subsequent work, p. 10.
Chapter 2. incidence
2 1 Primitive concepts, p. 12. 2 2 The axioms of incidence, p. 14. 2*3 The princi¬
ple of duality, p. 15. 2 4 Quadrangle and quadrilateral, p. 17. 2 5 Harmonic con
jugacy, p. 18. 2 6 Ranges and pencils, p. 21. 2 7 Perspectivity, p. 21. 2 8 The
invariance and symmetry of the harmonic relation, p. 23.
Chapter 3. order and continuity
3 1 The axioms of order, p. 25. 3 2 Segment and interval, p. 27. 3 3 Sense,
p. 29. 3 4 Ordered correspondence, p. 30. 3 5 Continuity, p. 34. 3 6 Invariant
points, p. 34. 3 7 Order in a pencil, p. 36. 3 8 The four regions determined by a
triangle, p. 37.
Chapter 4. one dimensional projectivities
4 1 Projectivity, p. 39. 4 2 The fundamental theorem of projective geometry,
p. 41. 4 3 Pappus s theorem, p. 43. 4 4 Classification of projectivities, p. 45.
4 5 Periodic projectivities, p. 48. 4 6 Involution, p. 48. 4 7 Quadrangular set of
six points, p. 52. 4 8 Projective pencils, p. 54.
Chapter 5. two dimensional projectivities
5 1 Collineation, p. 55. 5 2 Perspective collineation, p. 57. 5 3 Involutory
collineation, p. 59. 5 4 Correlation, p. 61. 5 5 Polarity, p. 62. 5 6 Polar and
self polar triangles, p. 66. 5 7 The self polarity of the Desargues configuration,
p. 68. 5 8 Pencil and range of polarities, p. 70. 5 9 Degenerate polarities, p. 71.
xi
xii CONTENTS
Chapter 6. conics
6 1 Historial remarks, p. 73. 6 2 Elliptic and hyperbolic polarities, p. 74. 6 3
How a hyperbolic polarity determines a conic, p. 76. 6 4 Conjugate points and
conjugate lines, p. 78. 6 5 Two possible definitions for a conic, p. 80. 6 6 Con¬
struction for the conic through five given points, p. 83. 6*7 Two triangles inscribed
in a conic, p. 85. 6 8 Pencils of conics, p. 87.
Chapter 7. projectivities on a conic
7 1 Generalized perspectivity, p. 92. 7 2 Pascal and Brianchon, p. 94. 7 3 Con¬
struction for a projectivity on a conic, p. 96. 7 4 Construction for the invariant
points of a given hyperbolic projectivity, p. 98. 7 5 Involution on a conic,
p. 99. 7 6 A generalization of Steiner s construction, p. 102. 7 7 Trilinear polar¬
ity, p. 103.
Chapter 8. apfine geometry
8 1 Parallelism, p. 105. 8 2 Intermediacy, p. 106. 8 3 Congruence, p. 107. 8 4
Distance, p. 109. 8 5 Translation and dilatation, p. 113. 8 6 Area, p. 114. 8 7
Classification of conics, p. 117. 8 8 Conjugate diameters, p. 119. 8 9 Asymptotes,
p. 121. 8 10 Affine transformations and the Erlangen programme, p. 124.
Chapter 9. Euclidean geometry
9 1 Perpendicularity, p. 126. 9 2 Circles, p. 128. 9 3 Axes of a conic, p. 131.
9 4 Congruent segments, p. 133. 9 5 Congruent angles, p. 134. 9 6 Congruent
transformations, p. 138. 9 7 Foci, p. 142. 9 8 Directrices, p. 144.
Chapter 10. continuity
10 1 An improved axiom of continuity, p. 147. 10 2 Proving Archimedes axiom,
p. 148. 10 3 Proving the line to be perfect, p. 149. 10 4 The fundamental theorem
of projective geometry, p. 152. 10 5 Proving Dedekind s axiom, p. 153. 10 6 En
riques s theorem, p. 153.
Chapter 11. the introduction of coordinates
11 1 Addition of points, p. 156. 11 2 Multiplication of points, p. 158. 11 3 Ratio¬
nal points, p. 161. 11 4 Projectivities, p. 161. 11 5 The one dimensional con¬
tinuum, p. 163. 11 6 Homogeneous coordinates, p. 165. 11 7 Proof that a line has
a linear equation, p. 165. 11 8 Line coordinates, p. 167.
Chapter 12. the use of coordinates
12 1 Consistency and categoricalness, p. 169. 12 2 Analytic geometry, p. 171.
12 3 Verifying the axioms of incidence, p. 173. 12 4 Verifying the axioms of order
CONTENTS xiii
and continuity, p. 174. 12 5 The general collineation, p. 178. 12 6 The general
polarity, p. 181. 12 7 Conies, p. 185. 12 8 The affine plane: affine and areal coor¬
dinates, p. 191. 12 9 The Euclidean plane: Cartesian and trilinear coordinates,
p. 193.
Appendix 1. The Complex Projective Plane page 200
Appendix 2. How to Use Mathematica® by George Beck 202
Bibliography 214
Index 217
|
| any_adam_object | 1 |
| author | Coxeter, Harold S. M. 1907-2003 |
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| author_variant | h s m c hsm hsmc |
| building | Verbundindex |
| bvnumber | BV008141827 |
| classification_rvk | SK 370 SK 380 |
| ctrlnum | (OCoLC)632456292 (DE-599)BVBBV008141827 |
| discipline | Mathematik |
| edition | Third edition |
| format | Book |
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| id | DE-604.BV008141827 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:15:14Z |
| institution | BVB |
| isbn | 0387978895 3540978895 |
| language | English |
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| publisher | Springer |
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| spelling | Coxeter, Harold S. M. 1907-2003 Verfasser (DE-588)118522507 aut The real projective plane PC version (Diskette provided) H. S. M. Coxeter. With an appendix for Mathematica by George Beck Third edition New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest Springer 1993 © 1993 xiii, 222 Seiten Illustrationen, Diagramme 1 Diskette, 5,25" txt rdacontent n rdamedia nc rdacarrier Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Ebene (DE-588)4150968-7 gnd rswk-swf Projektive Ebene (DE-588)4175884-5 gnd rswk-swf Projektive Ebene (DE-588)4175884-5 s DE-604 Projektive Geometrie (DE-588)4047436-7 s Ebene (DE-588)4150968-7 s 1\p DE-604 Beck, George wst HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005370966&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Coxeter, Harold S. M. 1907-2003 The real projective plane PC version (Diskette provided) Projektive Geometrie (DE-588)4047436-7 gnd Ebene (DE-588)4150968-7 gnd Projektive Ebene (DE-588)4175884-5 gnd |
| subject_GND | (DE-588)4047436-7 (DE-588)4150968-7 (DE-588)4175884-5 |
| title | The real projective plane PC version (Diskette provided) |
| title_auth | The real projective plane PC version (Diskette provided) |
| title_exact_search | The real projective plane PC version (Diskette provided) |
| title_full | The real projective plane PC version (Diskette provided) H. S. M. Coxeter. With an appendix for Mathematica by George Beck |
| title_fullStr | The real projective plane PC version (Diskette provided) H. S. M. Coxeter. With an appendix for Mathematica by George Beck |
| title_full_unstemmed | The real projective plane PC version (Diskette provided) H. S. M. Coxeter. With an appendix for Mathematica by George Beck |
| title_short | The real projective plane |
| title_sort | the real projective plane pc version diskette provided |
| title_sub | PC version (Diskette provided) |
| topic | Projektive Geometrie (DE-588)4047436-7 gnd Ebene (DE-588)4150968-7 gnd Projektive Ebene (DE-588)4175884-5 gnd |
| topic_facet | Projektive Geometrie Ebene Projektive Ebene |
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