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[资源] How To Fold It - The Math Of Linkages, Origami, Polyhedra

Preface page ix
PART I. Linkages 1
1 Robot Arms 3
1.1 Annulus 5
1.2 Reaching Angles 15
1.3 Above & Beyond 20
2 Straight-Line Linkages and the Pantograph 24
2.1 Straight-Line Linkages 24
2.2 Pantograph 28
2.3 Above & Beyond 36
3 Protein Folding and Pop-Up Cards 39
3.1 Fixed-Angle Chains 39
3.2 Protein Backbones 40
3.3 Maximum Span 42
3.4 Alignment 44
3.5 Piercing 46
3.6 Pop-Up Spinner 48
3.7 Above & Beyond 52
PART II. Origami 55
4 Flat Vertex Folds 57
4.1 Mountain and Valley Creases 57
4.2 Single-Vertex Flat Folds 58
4.3 The Maekawa-Justin Theorem 61
4.4 The Local Min Theorem 64
4.5 The Kawasaki-Justin Theorem 66
4.6 Above & Beyond 68
v
vi Contents
5 Fold and One-Cut 72
5.1 Examples 72
5.2 Fold and One-Cut Theorem 78
5.3 Above & Beyond 81
6 The Shopping Bag Theorem 84
6.1 Two Rigid Origami Examples 85
6.2 Dihedral Angle Constraints 89
6.3 The Shopping Bag Theorem 93
6.4 Above & Beyond 96
PART III. Polyhedra 99
7 Dürer’s Problem: Edge Unfolding 101
7.1 Albrecht Dürer’s Nets 101
7.2 Convex Polyhedra 103
7.3 The Open Problem 106
7.4 Spanning Cut Tree 109
7.5 Some Polyhedra with Nets 112
7.6 Above & Beyond 115
8 Unfolding Orthogonal Polyhedra 119
8.1 Orthogonal Polyhedra 119
8.2 Orthogonal Terrains 120
8.3 Grid Unfoldings 125
8.4 Above & Beyond 126
9 Folding Polygons to Convex Polyhedra 130
9.1 Questions 132
9.2 Alexandrov’s Theorem 133
9.3 Folding Convex Polygons 135
9.4 The Foldings of the Latin Cross 138
9.5 Above & Beyond 140
10 Further Reading 142
Glossary 147
Answers to Exercises 151
Chapter 1 151
Chapter 2 155
Chapter 3 156
Chapter 4 158
Chapter 5 161
Chapter 6 162
Contents vii
Chapter 7 165
Chapter 8 168
Chapter 9 170
Acknowledgments 173
Index 175

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附件 1 : How_To_Fold_It_-_The_Math_Of_Linkages,_Origami,_Polyhedra_(Cambridge,_2011).pdf

2015-09-06 11:51:43, 16.66 M