The nature of mathematics and the mathematics of nature:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
1998
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 345 S. Ill., graph. Darst. |
| ISBN: | 0444829946 |
Staff View
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Record in the Search Index
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| adam_text | THE NATURE OF MATHEMATICS AND THE MATHEMATICS OF NATURE BY MICHAEL JACOB
DEPARTMENT OF INORGANIC CHEMISTRY ARRHENIUS LABORATORY UNIVERSITY OF
STOCKHOLM S-10691 STOCKHOLM, SWEDEN AND STEN ANDERSSON SANDVIKS
FORSKNINGSINSTITUT S. LANGGATAN 27 S-38074 LOTTORP, SWEDEN 1998 ELSEVIER
AMSTERDAM. LAUSANNE. NEW YORK. OXFORD. SHANNON. SINGAPORE. TOKYO
CONTENTS CHAPTER 1 1 INTRODUCTION 1 REFERENCES 1 4 PUBLICATIONS ON THE
EXPONENTIAL SCALE 5 CHAPTER 2 2 THE ROOTS OF MATHEMATICS - THE ROOTS OF
STRUCTURE 7 2.1 MULTIPLICATION OF POLYNOMIALS 7 2.2 ADDITION OF
POLYNOMIALS 16 2.3 SADDLES 26 EXERCISES 2 31 REFERENCES 2 38 CHAPTER 3 3
THE NATURAL FUNCTION AND THE EXPONENTIAL SCALE 39 3.1 POLYGONS AND
PLANAR GEOMETRY 39 3.2 POLYHEDRA AND GEOMETRY 47 3.3 CURVATURE 52 3.4
THE FUNDAMENTAL POLYHEDRA - AND OTHERS 55 3.5 OPTIMAL ORGANISATION AND
HIGHER EXPONENTIALS 62 EXERCISES 3 67 REFERENCES 3 71 CHAPTER 4 4
PERIODICITY AND THE COMPLEX EXPONENTIAL 73 4.1 THE TRANSLATION VECTOR 73
4.2 THE COMPLEX EXPONENTIAL AND SOME VARIANTS 80 4.3 SOME OTHER
EXPONENTIALS 88 EXERCISES 4 94 REFERENCES 4 98 CHAPTERS 5 THE SCREW AND
THE FINITE PERIODICITY WITH THE CIRCULAR PUNCTIONS 99 5.1 CHIRALITY, THE
SCREW AND THE MULTI SPIRAL 99 5.2 THE BENDING OF A HELIX 109 5.3 FINITE
PERIODICITY - MOLECULES AND THE LARSSON CUBOSOMES 112 EXERCISES 5 119
REFERENCES 5 122 VI CONTENTS CHAPTER 6- 6 MULTIPLICATION, NETS AND
PLANAR GROUPS 123 6.1 LINES AND SADDLES 123 6.2 NETS WITH TWO PLANES,
AND VARIATIONS 125 6.3 NETS WITH THREE PLANES, AND VARIATIONS 127 6.4
NETS WITH FOUR PLANES, AND VARIATIONS 130 6.5 STRUCTURES IN 3D FROM THE
NETS 132 6.6 QUASI 136 6.6.1 FOUR PLANES AND QUASI 136 6.6.2 FIVE PLANES
AND QUASI 137 EXERCISES 6 139 REFERENCES 6 146 CHAPTER 7 7 THE GAUSS
DISTRIBUTION FUNCTION 147 7.1 THE GD FUNCTION AND PERIODICITY 147 7.1.1
HANDMADE PERIODICITY 155 7.2 THE GD FUNCTION AND PERIODICITY IN 3D 156
7.3 THE BCC AND DIAMOND SYMMETRIES 161 7.4 THE LINK TO COSINE 176
EXERCISES 7 186 REFERENCES 7 190 CHAPTER 8 8 HANDMADE STRUCTURES AND
PERIODICITY 191 8.1 PRELUDE 191 8.2 SIMPLEST OF PERIODIC STRUCTURES 201
8.3 CONTACT OF SPHERES IN SPACE - STRUCTURES AND SURFACES 205 8.4 HOW
TETRAHEDRA AND OCTAHEDRA MEET IN SPACE 226 EXERCISES 8 229 REFERENCES 8
236 CHAPTER 9 9 THE RODS IN SPACE 237 9.1 PRIMITIVE PACKING OF RODS 237
9.2 BODY CENTRED PACKING OF RODS 242 9.3 TETRAGONAL AND HEXAGONAL
PACKING OF RODS 246 9.4 LARSSON CUBOSOMES OF RODS 253 9.5 PACKING OF
RODS, AND THEIR RELATED SURFACES 258 EXERCISES 9 262 REFERENCES 9 265
CONTENTS VII CHAPTER 10 10 THE RINGS, ADDITION AND SUBTRACTION 267 10.1
SOME SIMPLE EXAMPLES OF SUBTRACTION AND ADDITION IN 3D 267 10.2 THE
RINGS 273 10.3 MORE WAYS TO MAKE RINGS 278 10.4 MORE SUBTRACTION -
HYPERBOLIC POLYHEDRA 283 EXERCISES 10 289 REFERENCES 10 292 CHAPTER 11
11 PERIODIC DILATATION - CONCENTRIC SYMMETRY 293 11.1 DILATATION AND
TRANSLATION IN 2D 293 11.2 DILATATION AND TRANSLATION IN 3D 300 11.3
PURE DILATATION 312 EXERCISES 11 320 REFERENCES 11 324 APPENDIX 1
MATHEMATICA 325 APPENDIX 2 CURVATURE AND DIFFERENTIAL GEOMETRY 327
APPENDIX 3 FORMAL WAY TO DERIVE THE SHAPES OF POLYHEDRA 330 APPENDIX 4
MORE CURVATURE 333 APPENDIX 5 RAISON D ETRE 335 SUBJECT INDEX 33 9
|
| any_adam_object | 1 |
| author | Jacob, Michael Andersson, Sten |
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| building | Verbundindex |
| bvnumber | BV012373910 |
| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)246232190 (DE-599)BVBBV012373910 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:26:27Z |
| institution | BVB |
| isbn | 0444829946 |
| language | English |
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| physical | VII, 345 S. Ill., graph. Darst. |
| publishDate | 1998 |
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| publisher | Elsevier |
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| spelling | Jacob, Michael Verfasser aut The nature of mathematics and the mathematics of nature by Michael Jacob and Sten Andersson Amsterdam [u.a.] Elsevier 1998 VII, 345 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf Mathematik (DE-588)4037944-9 s Naturwissenschaften (DE-588)4041421-8 s Modellierung (DE-588)4170297-9 s DE-604 Andersson, Sten Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008392131&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacob, Michael Andersson, Sten The nature of mathematics and the mathematics of nature Mathematik (DE-588)4037944-9 gnd Modellierung (DE-588)4170297-9 gnd Naturwissenschaften (DE-588)4041421-8 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4170297-9 (DE-588)4041421-8 |
| title | The nature of mathematics and the mathematics of nature |
| title_auth | The nature of mathematics and the mathematics of nature |
| title_exact_search | The nature of mathematics and the mathematics of nature |
| title_full | The nature of mathematics and the mathematics of nature by Michael Jacob and Sten Andersson |
| title_fullStr | The nature of mathematics and the mathematics of nature by Michael Jacob and Sten Andersson |
| title_full_unstemmed | The nature of mathematics and the mathematics of nature by Michael Jacob and Sten Andersson |
| title_short | The nature of mathematics and the mathematics of nature |
| title_sort | the nature of mathematics and the mathematics of nature |
| topic | Mathematik (DE-588)4037944-9 gnd Modellierung (DE-588)4170297-9 gnd Naturwissenschaften (DE-588)4041421-8 gnd |
| topic_facet | Mathematik Modellierung Naturwissenschaften |
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