Regular figures:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford u.a.
Pergamon Pr.
1964
|
| Schriftenreihe: | International series of monographs on pure and applied mathematics
48 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001687042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 339 S. Ill., zahlr. graph. Darst. XIII Beil. |
Internformat
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| 490 | 1 | |a International series of monographs on pure and applied mathematics |v 48 | |
| 650 | 4 | |a Decoration and ornament | |
| 650 | 4 | |a Symmetry | |
| 650 | 4 | |a Topology | |
| 650 | 4 | |a Transformations (Mathematics) | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0024 58 A 287-48 0102 MAT 052f 2001 A 14150 |
|---|---|
| DE-BY-TUM_katkey | 476263 |
| DE-BY-TUM_location | Mag 01 |
| DE-BY-TUM_media_number | TEMP2788798 040010696894 |
| _version_ | 1821938773575860224 |
| adam_text | CONTENTS
Preface jx
PART ONE
SYSTEMATOLOGY OF THE REGULAR FIGURES
I. Plane ornaments 3
1. Isometries 3
2. Symmetry groups 8
3. Groups with infinite unit cells 11
4. Groups with finite unit cells 21
5. Remarks , 38
II. Spherical arrangements 56
6. Isometries in space 56
7. The finite rotation groups 58
8. The finite symmetry groups 63
9. Groups of permutations 70
10. The geometrical crystal classes 78
11. Remarks 81
III. Hyperbolic tessellations 84
12. The hyperbolic plane 84
13. Hyperbolic trigonometry 91
14. Hyperbolic tessellations 95
15. Remarks 97
IV. POLYHEDRA 102
16. The nine regular polyhedra 102
17. Semi-regular polyhedra 108
18. Parallelohedra 114
19. Remarks 119
V. Regular polytopes 124
20. Geometry in more than three dimensions ... 124
21. The general regular poly tope 132
22. The convex regular polytopes 137
23. Remarks 144
PART TWO
GENETICS OF THE REGULAR FIGURES
VI: Figures in the euclideah plane 151
24. Inequalities for polygons 151
25. Packing and covering problems 160
vii
viii CONTENTS
26. Isoperimetric problems in cell-aggregates .... 172
27. Packings and coverings by non-congruent circles 183
28. A stability problem for circle-packings 198
29. Remarks 200
VII. Spherical figures 213
30. The isoperimetric property of the regular
spherical polygons 213
31. Shortest spherical net with meshes of equal
area 215
32. An extremal distribution of great circles .... 216
33. An inequality for star-tessellations 219
34. A covering problem 224
35. Distribution of the orifices on pollen-grains. . . 226
36. Remarks 235
VIII. Problems in the hyperbolic plane 238
37. Circle-packings and circle-coverings 238
38. Packing and covering by horocycles 247
39. An extremum property of the tessellations {p, 3} 254
40. Remarks 261
IX. Problems in 3-space 263
41. Volume estimates for polyhedra 263
42. Surface area and edgecurvature 278
43. The isoperimetric problem for polyhedra .... 282
44. Sphere-clouds 288
45. Sphere-packings and sphere-coverings 292
46. Honeycombs 300
47. Remarks 304
X. Problems in higher spaces 308
48. On the volume of a polyhedron in non-Euc¬
lidean 3-space 308
49. Extremum properties of the regular polytopes 312
•50. Sphere-packings and sphere-coverings in spaces
of constant curvature 317
51. Remarks 323
Postscript 326
Bibliography 327
Index 333
|
| any_adam_object | 1 |
| author | Fejes Tóth, László |
| author_facet | Fejes Tóth, László |
| author_role | aut |
| author_sort | Fejes Tóth, László |
| author_variant | t l f tl tlf |
| building | Verbundindex |
| bvnumber | BV002625337 |
| callnumber-first | Q - Science |
| callnumber-label | QA601 |
| callnumber-raw | QA601 |
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| callnumber-sort | QA 3601 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)718938 (DE-599)BVBBV002625337 |
| 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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| id | DE-604.BV002625337 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:52:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001687042 |
| oclc_num | 718938 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-824 DE-29T DE-634 DE-83 DE-11 DE-188 DE-210 |
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| physical | XI, 339 S. Ill., zahlr. graph. Darst. XIII Beil. |
| psigel | TUB-nvmb |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Pergamon Pr. |
| record_format | marc |
| series | International series of monographs on pure and applied mathematics |
| series2 | International series of monographs on pure and applied mathematics |
| spellingShingle | Fejes Tóth, László Regular figures International series of monographs on pure and applied mathematics Decoration and ornament Symmetry Topology Transformations (Mathematics) Polyeder (DE-588)4132101-7 gnd Geometrische Figur (DE-588)4139878-6 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd |
| subject_GND | (DE-588)4132101-7 (DE-588)4139878-6 (DE-588)4186551-0 |
| title | Regular figures |
| title_auth | Regular figures |
| title_exact_search | Regular figures |
| title_full | Regular figures L. Fejes Tóth |
| title_fullStr | Regular figures L. Fejes Tóth |
| title_full_unstemmed | Regular figures L. Fejes Tóth |
| title_short | Regular figures |
| title_sort | regular figures |
| topic | Decoration and ornament Symmetry Topology Transformations (Mathematics) Polyeder (DE-588)4132101-7 gnd Geometrische Figur (DE-588)4139878-6 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd |
| topic_facet | Decoration and ornament Symmetry Topology Transformations (Mathematics) Polyeder Geometrische Figur Überdeckung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001687042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT fejestothlaszlo regularfigures |
Inhaltsverzeichnis
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Bibliotheksmagazin
| Signatur: |
0024 58 A 287-48 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 052f 2001 A 14150 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |