Geometry: euclid and beyond:
Gespeichert in:
| Vorheriger Titel: | Hartshorne, Robin Companion to Euclid: a course of geometry, based on Euclid's elements and its modern descendants |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 526 S. Ill., graph. Darst 25 cm |
| ISBN: | 0387986502 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804138973634756608 |
|---|---|
| adam_text | ROBIN HARTSHORNE GEOMETRY: EUCLID AND BEYOND WITH 550 ILLUSTRATIONS 4U
SPRINGER CONTENTS INTRODUCTION CHAPTER 1. EUCLID S GEOMETRY 1. A FIRST
LOOK AT EUCLID S ELEMENTS 2. RULER AND COMPASS CONSTRUCTIONS 3. EUCLID S
AXIOMATIC METHOD 4. CONSTRUCTION OF THE REGULAR PENTAGON 5. SOME NEWER
RESULTS 8 18 27 45 51 CHAPTER 2. HILBERT S AXIOMS 6. AXIOMS OF INCIDENCE
7. AXIOMS OF BETWEENNESS 8. AXIOMS OF CONGRUENCE FOR LINE SEGMENTS 9.
AXIOMS OF CONGRUENCE FOR ANGLES 10. HILBERT PLANES 11. INTERSECTION OF
LINES AND CIRCLES 12. EUCLIDEAN PLANES 65 66 73 81 90 96 104 112 CHAPTER
3. GEOMETRY OVER FIELDS 13. THE REAL CARTESIAN PLANE 14. ABSTRACT FIELDS
AND INCIDENCE 15. ORDERED FIELDS AND BETWEENNESS 117 118 128 135 IX
CONTENTS 16. CONGRUENCE OF SEGMENTS AND ANGLES 140 17. RIGID MOTIONS AND
SAS 148 18. NON-ARCHIMEDEAN GEOMETRY 158 CHAPTER 4. SEGMENT ARITHMETIC
165 19. ADDITION AND MULTIPLICATION OF LINE SEGMENTS 165 20. SIMILAR
TRIANGLES 175 21. INTRODUCTION OF COORDINATES 186 CHAPTER 5. AREA 195
22. AREA IN EUCLID S GEOMETRY 196 23. MEASURE OF AREA FUNCTIONS 205 24.
DISSECTION 212 25. QUADRATURE CIRCULI 221 26. EUCLID S THEORY OF VOLUME
226 27. HILBERT S THIRD PROBLEM 231 CHAPTER 6. CONSTRUCTION PROBLEMS AND
FIELD EXTENSIONS 241 28. THREE FAMOUS PROBLEMS 242 29. THE REGULAR
17-SIDED POLYGON 250 30. CONSTRUCTIONS WITH COMPASS AND MARKED RULER 259
31. CUBIC AND QUARTIC EQUATIONS 270 32. APPENDIX: FINITE FIELD
EXTENSIONS 280 CHAPTER 7. NON-EUCLIDEAN GEOMETRY 295 33. HISTORY OF THE
PARALLEL POSTULATE 296 34. NEUTRAL GEOMETRY 304 35. ARCHIMEDEAN NEUTRAL
GEOMETRY 319 36. NON-EUCLIDEAN AREA 326 37. CIRCULAR INVERSION 334 38.
DIGRESSION: CIRCLES DETERMINED BY THREE CONDITIONS 346 39. THE POINCARE
MODEL 355 40. HYPERBOLIC GEOMETRY 373 41. HILBERT S ARITHMETIC OF ENDS
388 42. HYPERBOLIC TRIGONOMETRY 403 43. CHARACTERIZATION OF HILBERT
PLANES 415 CHAPTER 8. POLYHEDRA 435 44. THE FIVE REGULAR SOLIDS 436 45.
EULER S AND CAUCHY S THEOREMS 448 CONTENTS 46. SEMIREGULAR AND
FACE-REGULAR POLYHEDRA 459 47. SYMMETRY GROUPS OF POLYHEDRA 469
APPENDIX: BRIEF EUCLID 481 NOTES 487 REFERENCES 495 LIST OF AXIOMS 503
INDEX OF EUCLID S PROPOSITIONS 505 INDEX 507
|
| any_adam_object | 1 |
| author | Hartshorne, Robin 1938- |
| author_GND | (DE-588)133225089 |
| author_facet | Hartshorne, Robin 1938- |
| author_role | aut |
| author_sort | Hartshorne, Robin 1938- |
| author_variant | r h rh |
| building | Verbundindex |
| bvnumber | BV023782313 |
| classification_rvk | SK 370 SK 380 |
| ctrlnum | (OCoLC)247577065 (DE-599)BVBBV023782313 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T21:36:42Z |
| institution | BVB |
| isbn | 0387986502 |
| language | English |
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| physical | XI, 526 S. Ill., graph. Darst 25 cm |
| publishDate | 2000 |
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| series2 | Undergraduate texts in mathematics |
| spelling | Hartshorne, Robin 1938- Verfasser (DE-588)133225089 aut Geometry: euclid and beyond Robin Hartshorne New York [u.a.] Springer 2000 XI, 526 S. Ill., graph. Darst 25 cm txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Geometrie (DE-588)4020236-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Geometrie (DE-588)4020236-7 s DE-604 Früher u.d.T. Hartshorne, Robin Companion to Euclid: a course of geometry, based on Euclid's elements and its modern descendants HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017424525&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hartshorne, Robin 1938- Geometry: euclid and beyond Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4123623-3 |
| title | Geometry: euclid and beyond |
| title_auth | Geometry: euclid and beyond |
| title_exact_search | Geometry: euclid and beyond |
| title_full | Geometry: euclid and beyond Robin Hartshorne |
| title_fullStr | Geometry: euclid and beyond Robin Hartshorne |
| title_full_unstemmed | Geometry: euclid and beyond Robin Hartshorne |
| title_old | Hartshorne, Robin Companion to Euclid: a course of geometry, based on Euclid's elements and its modern descendants |
| title_short | Geometry: euclid and beyond |
| title_sort | geometry euclid and beyond |
| topic | Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometrie Lehrbuch |
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