Concepts of geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Delhi
Hindustan Publ.
1976
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 260 Seiten |
Internformat
MARC
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| 100 | 1 | |a Datta, Dilip K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Concepts of geometry |c Dilip Kumar Datta |
| 264 | 1 | |a Delhi |b Hindustan Publ. |c 1976 | |
| 300 | |a XII, 260 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Geometry |x Foundations |x Study and teaching | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001423259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001423259 | ||
Datensatz im Suchindex
| _version_ | 1804116622895480832 |
|---|---|
| adam_text | Contents
Preface v
Chapter 0. INTRODUCTION x?
Chapter 1. AXIOMATIC METHOD 1
§ 1. Projective Plane 1
§ 2. Affine Plane 3
§ 3. Models 4
3.1. Simplicity 6
3.2. Independence 6
3.3. Consistency 7
3.4. Completeness 7
3.5. Categorical 7
§ 4. Finite Projective Planes 8
4.1. Exercises 12
§ 5. Latin Squares and Euler Conjecture 13
5.1. Example 20
5.2. Exercises 21
§ 6. Euclidean Geometry 22
6.1. Undefined elements of Euclidean geometry 23
6.2. Euclid s axioms 23
6.3. Criticism 23
6.4. Contents of axiomatic systems to replace Euclid s axioms 25
6.5. Concept of distance 26
6.6. Distance]on Euclidean plane 27
6.7. Order on Euclidean plane 28
6.8. Angle on Euclidean plane 28
6.9. Axioms of continuity and completeness 28
6.10 Exercises 30
§ 7. Non Euclidean Geometry 32
7.1. Three Non Euclidean Geometries 33
7.2. Exercises 37
X
Chapter 2. SYNTHETIC PROJECTIVE GEOMETRY 40
§ 8. Terminology and Notation 40
§ 9. The Principle of Duality 40
9.1. Exercises 41
§ 10. Configurations and Fano s Axiom 42
§11. Quadrangle and Quadrilateral 44
11.1. Exercises 47
§ 12. Desargues Axiom 48
12.1. Exercises 51
§ 13. Harmonic Sets 51
13.1. Exercises 55
§ 14. Axioms of Order 56
14.1. Exercises 60
§15. Perspectivity and Projectivity . 61
15.1. Introduction 61
15.2. Definitions and Theorems 61
15.3. Exercises 70
§ 16. Net of Rationality and Continuity Axiom 71
16.1. Definitions and Theorems 71
16.2. Exercises 77
Chapter 3. ANALYTIC PROJECTIVE GEOMETRY 78
§ 17. Algebraic Preliminaries 78
17.1. Definitions and Theorem 78
17.2. Exercises 82
§ 18. Matrices and Determinants 83
18.1. Matrices 83
18.2. Determinants 88
18.3. Examples 92
18.4. Matrices (Revisited) 93
18.5. Example 94
18.6. Exercises 94
18.7. Applications 97
18.8. Examples , 98
18.9. Linear Transformation of Rn 100
18.10. Exercises 101
xi
§ 19. Equivalence Relation 102
19.1. Examples 103
19.2. Exercises 104
§ 20. Analytic Projective Plane 105
20.1. Exercises 108
§21. Coordinates for P2 109
21.1. Exercises 112
§22. Coordinate System for a Line 113
22.1. Examples 114
§23. Desargues Axiom 116
§24. Change of Coordinates 117
§25. Non Singular Linear Transformations of /f2 121
25.1. Example 122
25.2. Exercises 123
§ 26. Cross Ratio 124
§27. Projective Transformations of a Line onto itself 130
27.1. Exercises 131
§ 28. Polarities and Conies 132
28.1. Intersection of a Line and a Conic 134
28.2. Example 136
28.3. Exercises 137
Chapter 4. ERLANGER PROGRAM 140
§29. Group of Transformations 140
29.1. Example 140
29.2. Exercises 141
§30. Group of Projective Transformations 142
30.1. Example 145
30.2. Exercises 146
§31. Subgroups 147
31.1. Example . 147
31.2. Exercises 148
§ 32. Analytic Affine Plane 148
xii
§33. Classification of Conies 154
33.1. Example 155
33.2. Exercises 157
§ 34. Euclidean Plane and the Group of Euclidean
Transformations 158
34.1. Exercises 162
§35. Other Subgeometries of Projective Geometry 162
35.1. Exercises 165
35.2. Tree diagram 165
Chapter 5. TOPOLOGY—A NEW GEOMETRY 166
§ 36. Topological Spaces 166
36.1. Examples 167
36.2. Examples 169
36.3. Examples 170
36.4. Exercises 171
§ 37. Continuous Transformations 171
37.1. Examples 172
37.2. Exercises 174
§ 38. Homeomorphisms 174
38.1. Example 175
38.2. Exercises 175
§ 39. Product Topology 175
39.1. Examples 176
39.2. Examples 178
39.3. Exercises 179
§ 40. Identification Topology 180
40.1. Examples 180
40.2. Exercises 182
§ 41. Topology of the Projective Plane 182
Chapter 6. HIGHER DIMENSIONAL SPACES 187
§ 42. Vector Spaces 187
42.1. Examples of Vector Spaces 188
42.2. Complex Numbers 190
42.3. Exercises 191
42.4. Examples 194
42.5. Exercises 195
§ 43. n Dimensional Euclidean Space 196
43.1. Introduction 196
43.2. The Spaced3 198
43.3. Exercises 201
§ 44. Euclidean Transformations 202
44.1. Examples 205
44.2. Exercises 206
§ 45. H Dimensional Affine Space 207
45.1. Introduction 207
45.2. Example 211
45.3. Exercises 211
§ 46. n Dimensional Projective Space 212
46.1. Example 213
46.2. Exercises 215
§ 47. Topology of Higher Dimensional Spaces 215
REFERENCES 218
APPENDIX 220
1. Definitions, Postulates 220
2. Hilbert s Axioms 225
3. Birkhoff s Postulates 232
4. S M S G Postulate 233
ANSWERS AND HINTS 237
INDEX 255
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:41:27Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001423259 |
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| physical | XII, 260 Seiten |
| publishDate | 1976 |
| publishDateSearch | 1976 |
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| publisher | Hindustan Publ. |
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| spelling | Datta, Dilip K. Verfasser aut Concepts of geometry Dilip Kumar Datta Delhi Hindustan Publ. 1976 XII, 260 Seiten txt rdacontent n rdamedia nc rdacarrier Geometry Foundations Study and teaching HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001423259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Datta, Dilip K. Concepts of geometry Geometry Foundations Study and teaching |
| title | Concepts of geometry |
| title_auth | Concepts of geometry |
| title_exact_search | Concepts of geometry |
| title_full | Concepts of geometry Dilip Kumar Datta |
| title_fullStr | Concepts of geometry Dilip Kumar Datta |
| title_full_unstemmed | Concepts of geometry Dilip Kumar Datta |
| title_short | Concepts of geometry |
| title_sort | concepts of geometry |
| topic | Geometry Foundations Study and teaching |
| topic_facet | Geometry Foundations Study and teaching |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001423259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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