Foundations of three-dimensional Euclidean geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1980
|
| Series: | Pure and applied mathematics.
56 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 268 S. graph. Darst. |
| ISBN: | 0824769015 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804116721501470720 |
|---|---|
| adam_text | CONTENTS
CHAPTER 0. INTRODUCTION 1
§1. The Axiomatic Method and Its Utilization in
Euclidean Geometry 1
a. The axiomatic method 1
b. Axiomatics of Euclidean geometry 6
§2. Useful Notions from Other Mathematical Theories 9
a. Binary relations 9
b. Groups 11
c. Fields and linear spaces 13
d. Topological spaces 17
CHAPTER 1. AFFINE SPACES 21
§1. Incidence Axioms and Their Consequences 21
§2. The Axiom of the Parallels and Its Influence on the
Incidence Properties 26
a. Affine spaces 26
b. Projective spaces 30
c. Desargues theorems 32
vii
viii CONTENTS
§3. The Fundamental Algebraic Structures of an Affine
Space 40
a. Vectors of an affine space 40
b. The vector sum 44
c. Scalars of an affine space 47
d. Scalar algebraic operations 51
e. Properties of the scalar field 54
§4. Coordinates in Affine Spaces 59
a. The linear space structure 59
b. Frames and coordinates 62
c. Affine spaces over a field 68
§5. Affine Transformations 73
a. Characteristic properties of affine transformations 73
b. Special affine transformations 76
c. The structure of the affine group 80
d. Determination of afrine transformations 85
PROBLEMS 90
CHAPTER 2. ORDERED SPACES 95
§1. The Order Axioms and Their First Consequences 95
a. Linear Order Properties 95
b. Plane and Spatial Order Properties 103
§2. Polygons and Polyhedra 110
a. Convex Polygons 110
b. The Jordan separation theorem 116
c. Problems on polyhedra 122
§3. Ordered Affine Spaces 128
a. Equivalent order axioms 128
b. Determination of the ordered affine spaces 135 (
c. Orientation of ordered affine spaces 143
CONTENTS ix
§4. Continuity Axioms 150
a. The Dedekind continuity axiom 150
b. Continuously ordered spaces 152
c. The axioms of Archimedes and Cantor 160
PROBLEMS 167
CHAPTER 3. EUCLIDEAN SPACES 171
§1. The Congruence Axioms and Their Relations with the
Incidence and Order Axioms 171
a. A preliminary discussion of congruence 171
b. Elementary properties of congruence of segments 174
c. The Euclidean group of a line 177
d. Plane congruence properties 180
e. Miscellaneous congruence properties 186
§2. Euclidean Spaces 193
a. Congruence and the parallel axiom 193
b. The scalar field of an Euclidean space 196
c. Euclidean structures and quadratic forms 202
d. Real Euclidean space 209
e. Absolute geometry 211
§3. A Short History of the Parallel Axiom 219
a. Historical discussion 219
b. Mathematical discussion 225
§4. The Independence of the Parallel Axiom 239
PROBLEMS 252
HINTS FOR SOLVING THE PROBLEMS 257
REFERENCES 26S
INDEX 267
|
| any_adam_object | 1 |
| author | Vaisman, Izu |
| author_facet | Vaisman, Izu |
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| ctrlnum | (OCoLC)6603057 (DE-599)BVBBV002263886 |
| dewey-full | 516.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.2 |
| dewey-search | 516.2 |
| dewey-sort | 3516.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002263886 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:01Z |
| institution | BVB |
| isbn | 0824769015 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001487750 |
| oclc_num | 6603057 |
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| physical | IX, 268 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics. |
| series2 | Pure and applied mathematics. |
| spelling | Vaisman, Izu Verfasser aut Foundations of three-dimensional Euclidean geometry Izu Vaisman New York [u.a.] Dekker 1980 IX, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics. 56 Exercice géométrie Géométrie - Fondements Géométrie - Fondements ram Géométrie euclidienne Geometry Foundations Geometrie (DE-588)4020236-7 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf Euklidische Geometrie (DE-588)4137555-5 s DE-604 Grundlage (DE-588)4158388-7 s Geometrie (DE-588)4020236-7 s Pure and applied mathematics. 56 (DE-604)BV000001885 56 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487750&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vaisman, Izu Foundations of three-dimensional Euclidean geometry Pure and applied mathematics. Exercice géométrie Géométrie - Fondements Géométrie - Fondements ram Géométrie euclidienne Geometry Foundations Geometrie (DE-588)4020236-7 gnd Grundlage (DE-588)4158388-7 gnd Euklidische Geometrie (DE-588)4137555-5 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4158388-7 (DE-588)4137555-5 |
| title | Foundations of three-dimensional Euclidean geometry |
| title_auth | Foundations of three-dimensional Euclidean geometry |
| title_exact_search | Foundations of three-dimensional Euclidean geometry |
| title_full | Foundations of three-dimensional Euclidean geometry Izu Vaisman |
| title_fullStr | Foundations of three-dimensional Euclidean geometry Izu Vaisman |
| title_full_unstemmed | Foundations of three-dimensional Euclidean geometry Izu Vaisman |
| title_short | Foundations of three-dimensional Euclidean geometry |
| title_sort | foundations of three dimensional euclidean geometry |
| topic | Exercice géométrie Géométrie - Fondements Géométrie - Fondements ram Géométrie euclidienne Geometry Foundations Geometrie (DE-588)4020236-7 gnd Grundlage (DE-588)4158388-7 gnd Euklidische Geometrie (DE-588)4137555-5 gnd |
| topic_facet | Exercice géométrie Géométrie - Fondements Géométrie euclidienne Geometry Foundations Geometrie Grundlage Euklidische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487750&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT vaismanizu foundationsofthreedimensionaleuclideangeometry |