Shaping space: exploring polyhedra in nature, art, and the geometrical imagination
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | X, 341 S. Ill., graph. Darst. |
| ISBN: | 9780387927138 |
Internformat
MARC
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| 245 | 1 | 0 | |a Shaping space |b exploring polyhedra in nature, art, and the geometrical imagination |c Marjorie Senechal ed. ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2013 | |
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Datensatz im Suchindex
| _version_ | 1804150408235450368 |
|---|---|
| adam_text | Contents
Part I First Steps
1
Introduction to the Polyhedron Kingdom
....................................... 3
Marjorie Senechal
2
Six Recipes for Making Polyhedra
............................................. 13
Marion Walter, Jean Pedersen, Magnus Wenninger, Doris
Schattschneider,
Arthur L. Loeb, Erik Demaine, Martin Demaine, and
Vi
Hart
3
Regular and Semiregular Polyhedra
............................................ 41
H.S.M. Coxeter
A Milestones in the History of Polyhedra
.......................................... 53
Joseph Malkevitch
5
Polyhedra: Surfaces or Solids?
................................................ 65
Arthur L. Loeb
6
Durer s Problem
............................................................. 77
Joseph O Rourke
Part II Polyhedra in Nature and Art
7
Exploring the Polyhedron Kingdom
............................................ 89
Marjorie Senechal
8
Spatial Perception and Creativity
.............................................. 109
Janos Baracs
9
Goldberg Polyhedra
.......................................................... 125
George Hart
10
Polyhedra and Crystal Structures
.............................................. 139
Chung Chieh
11
Polyhedral Molecular Geometries
.............................................. 153
Magdolna Hargittai
and
István Hargittai
12
Form, Function, and Functioning
.............................................. 171
George Fleck
vi
Contents
Part III Polyhedra in the Geometrical Imagination
13
The Polyhedron Kingdom Tomorrow
........................................... 193
Marjorie Senechal
14
Paneled and Molecular Polyhedra: How Stable Are They?
........................ 201
Ileana Streinu
15
Duality of Polyhedra
......................................................... 211
Branko
Grünbaum
and
G.C. Shephard
16
Combinatorial Prototiles
...................................................... 217
Egon Schulte
17
Polyhedra Analogues of the Platonic Solids
...................................... 223
Jörg
M.
Wills
18
Convex Polyhedra, Dirichlet Tessellations, and Spider Webs
...................... 231
Walter Whiteley, Peter F. Ash, Ethan Bolker, and Henry Crapo
19
Uniform Polyhedra from Diophantine Equations
................................ 253
Barry Monson
20
Torus Decompostions of Regular Polytopes in 4-space
............................ 257
Thomas F. Banchoff
21
Tensegrities and Global Rigidity
............................................... 267
Robert Connelly
22
Ten Problems in Geometry
.................................................... 279
Moritz
W.
Schmitt
and
Günter
M.
Ziegler
1.
Unfolding Polytopes
...................................................... 279
2.
Almost Disjoint Triangles
................................................. 280
3.
Representing Polytopes with Small Coordinates
............................... 281
4.
Polyhedra that Tile Space
.................................................. 282
5.
Fatness
................................................................. 283
6.
The
Hirsch
Conjecture
.................................................... 284
7.
Unimodality
............................................................. 285
8.
Decompositions of the Cube
............................................... 286
9.
The Ball-and-Cube Problem
................................................ 287
10.
The 3d Conjecture
........................................................ 288
Notes and References
............................................................. 291
Sources and Acknowledgments
.................................................... 321
Index
........................................................................... 327
Marjorie Senechal
Editor
SHAPING SPACE
Exploring Polyhedra in Nature, Art, and the Geometrical Imagination
.Molecules, galaxies, art galleries, sculptures, viruses, crys¬
tals, architecture, and more: Slniping Space
—
Exploring Poly¬
hedra in
Sature,
Art, and tite Geometrical Imagination is
an exuberant survey of polyhedra and at the same time a
hands-on, mind-boggling introduction to one of the oldest
and most fascinating branches of mathematics.
Some of the world s leading geometers present a treasury
of ideas, history, and culture to make the beauty of polyhe¬
dra accessible to students, teachers, polyhedra hobbyists,
and professionals such as architects and designers, painters
and sculptors, biologists and chemists, crystallographers,
physicists and earth scientists, engineers and model build¬
ers, mathematicians and computer scientists.
The creative chapters by more than
25
authors explore al¬
most every imaginable side of polyhedra. From the beauty
of natural forms to the monumental constructions made bv
man, there is something to fascinate every reader. The book
is dedicated to the memory of the legendary geometer
H. S.
ΛΙ.
Coxeter and the multifaceted design scientist
Arthur L. Loeb.
|
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| ctrlnum | (OCoLC)854715763 (DE-599)BVBBV041044974 |
| discipline | Mathematik |
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| spellingShingle | Shaping space exploring polyhedra in nature, art, and the geometrical imagination Raumvorstellung (DE-588)4121556-4 gnd Kunst (DE-588)4114333-4 gnd Geometrische Figur (DE-588)4139878-6 gnd Natur (DE-588)4041358-5 gnd Raumwahrnehmung (DE-588)4076536-2 gnd |
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| title | Shaping space exploring polyhedra in nature, art, and the geometrical imagination |
| title_auth | Shaping space exploring polyhedra in nature, art, and the geometrical imagination |
| title_exact_search | Shaping space exploring polyhedra in nature, art, and the geometrical imagination |
| title_full | Shaping space exploring polyhedra in nature, art, and the geometrical imagination Marjorie Senechal ed. ... |
| title_fullStr | Shaping space exploring polyhedra in nature, art, and the geometrical imagination Marjorie Senechal ed. ... |
| title_full_unstemmed | Shaping space exploring polyhedra in nature, art, and the geometrical imagination Marjorie Senechal ed. ... |
| title_short | Shaping space |
| title_sort | shaping space exploring polyhedra in nature art and the geometrical imagination |
| title_sub | exploring polyhedra in nature, art, and the geometrical imagination |
| topic | Raumvorstellung (DE-588)4121556-4 gnd Kunst (DE-588)4114333-4 gnd Geometrische Figur (DE-588)4139878-6 gnd Natur (DE-588)4041358-5 gnd Raumwahrnehmung (DE-588)4076536-2 gnd |
| topic_facet | Raumvorstellung Kunst Geometrische Figur Natur Raumwahrnehmung Aufsatzsammlung |
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