A background (natural, synthetic and algebraic) to geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Univ. Press
1967
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 342 S. |
Internformat
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| 246 | 1 | 3 | |a A background to geometry |
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| 300 | |a VIII, 342 S. | ||
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Datensatz im Suchindex
| _version_ | 1804126137543032832 |
|---|---|
| adam_text | CONTENTS
Preface poge v
Introduction 1
Book 1. Geometry without numbers
1.1 The set of points; collinear subsets 11
1.2 Various notations: the axioms of incidence 17
1.3 The Desargues figure 24
1.4 The harmonic transformer, 3f 34
1.5 Parallels 38
1.6 Separation, betweenness, order 42
1.7 Segments and regions 62
1.8 Sense 79
Excursus: book 1
1.1 Some finite geometries 84
1.2 A geometry in which collinear sets are circles 94
1.3 A finite non Desarguesian geometry 97
1.4 Geometry of three dimensions and the plane Desargues
figure 103
1.5 Some special three dimensional geometries 110
Book 2. Geometry and Counting
2.1 Displacement: the geometric transformer, 117
2.2 The primary nets on a line, 9ZR and 9£p 124
2.3 The primary net in the plane 138
2.4 Affine co ordinates and invariants 145
2.5 Involutions: the geometric transformer £ 160
2.6 Perpendiculars 176
Excursus: book 2
2.1 Co ordinate geometry in primary nets 181
2.2 A non Desarguesian co ordinate geometry 188
Viii CONTENTS
2.3 Projectivities and the cyclic generation of some finite
primary planar nets page 192
2.4 Polar systems in the planar net. The transformer St 200
Book 3. Geometry and Algebra
3.1 Introduction: the displacement transformer, 3) 219
3.2 The multiplication transformer, ^4t 224
3.3 The transformers Si and ~# and algebraic fields 229
3.4 The extension of the primary field consequent on the
adjunction of one point 233
3.5 General extensions, commutativity and Pappus:
quaternions 240
Excursus: booh 3
3.1 Some extensions of finite primary fields 251
3.2 Various extensions of finite planar primary nets 255
3.3 Q 9 and Q » * and their relations to T 9 264
Book 4. Congruence
4.1 The reflection transformer, 0t 275
4.2 The matrix representation of reflections 288
4.3 Length, area, angle in the surdic and real nets 294
Excursus: book 4
4.1 Congruence without displacements 305
Recapitulation 314
Diagrams 317
Notations 339
Index 341
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:40Z |
| institution | BVB |
| language | English |
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| physical | VIII, 342 S. |
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| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Univ. Press |
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| spelling | Room, Thomas Gerald Verfasser aut A background (natural, synthetic and algebraic) to geometry by T. G. Room A background to geometry Cambridge Univ. Press 1967 VIII, 342 S. txt rdacontent n rdamedia nc rdacarrier Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007819693&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Room, Thomas Gerald A background (natural, synthetic and algebraic) to geometry Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 |
| title | A background (natural, synthetic and algebraic) to geometry |
| title_alt | A background to geometry |
| title_auth | A background (natural, synthetic and algebraic) to geometry |
| title_exact_search | A background (natural, synthetic and algebraic) to geometry |
| title_full | A background (natural, synthetic and algebraic) to geometry by T. G. Room |
| title_fullStr | A background (natural, synthetic and algebraic) to geometry by T. G. Room |
| title_full_unstemmed | A background (natural, synthetic and algebraic) to geometry by T. G. Room |
| title_short | A background (natural, synthetic and algebraic) to geometry |
| title_sort | a background natural synthetic and algebraic to geometry |
| topic | Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007819693&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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