9780521525749

Flexagons Inside Out

by
  • ISBN13:

    9780521525749

  • ISBN10:

    0521525748

  • Format: Paperback
  • Copyright: 2003-09-15
  • Publisher: Cambridge University Press
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Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

Summary

Flexagons, paper models that can be bent in different ways to change their shape, are easy to make and work in surprising ways. This book contains numerous diagrams that the reader can photocopy and use to construct a variety of fascinating flexagons. The author also explains the mathematics behind these amazing creations. Although knowledge of the technical details requires a mathematical background, the models can be made and used by anyone. Flexagons appeals to all readers interested in puzzles and recreational mathematics.

Table of Contents

Preface ix
List of notation xi
Introduction 1(4)
1 Malting and flexing flexagons 5(9)
1.1 The trihexaflexagon
5(1)
1.2 The pinch flex
6(1)
1.3 A simple square flexagon
7(1)
1.4 General assembly instructions
8(5)
1.5 Decoration of faces
13(1)
2 Early history of flexagons 14(4)
2.1 The discovery of flexagons
14(1)
2.2 The Flexagon Committee
15(1)
2.3 Revival of interest
16(2)
3 Geometry of flexagons 18(13)
3.1 Flexagon characteristics
19(1)
3.2 Appearance of main positions
20(1)
3.3 Flexagons as linkages
21(3)
3.4 Mapping flexagons
24(5)
3.5 Flexagon figures and symbols
29(2)
4 Hexaflexagons 31(16)
4.1 Degrees of freedom of hexaflexagons
32(1)
4.2 The trihexaflexagon revisited
33(3)
4.3 Multicycle hexaflexagons
36(4)
4.4 Hexaflexagon design
40(2)
4.5 Hexaflexagon face arrangements
42(5)
5 Hexaflexagon variations 47(6)
5.1 Triangle flexagons
47(2)
5.2 The Vflex
49(3)
5.3 Origami with hexaflexagons
52(1)
6 Square flexagons 53(29)
6.1 Single cycle square flexagons
54(4)
6.2 Reconstruction from a flexagon figure
58(1)
6.3 Square flexagons with main position links
59(10)
6.4 Distinct types of square flexagon with main position links
69(1)
6.5 Square flexagons with box position links
70(6)
6.6 Square flexagon face arrangements
76(2)
6.7 The interleaf flex
78(4)
7 Introduction to convex polygon flexagons 82(14)
7.1 The convex polygon family
83(1)
7.2 Degrees of freedom of intermediate positions
84(3)
7.3 The digon flexagon
87(3)
7.4 Triangle flexagons revisited
90(3)
7.5 Square flexagons revisited
93(3)
8 Typical convex polygon flexagons 96(23)
8.1 Characteristics of typical convex polygon flexagons
97(1)
8.2 Pentagon flexagons
98(8)
8.3 Hexagon flexagons
106(4)
8.4 Octagon flexagons
110(9)
9 Ring flexagons 119(18)
9.1 Star flexagons
120(1)
9.2 The ring flexagon family
121(2)
9.3 Compound flexagons
123(3)
9.4 Compound square flexagons
126(2)
9.5 Compound pentagon flexagons
128(4)
9.6 Compound hexagon flexagons
132(5)
10 Distorted polygon flexagons 137(17)
10.1 Distorted polygons
137(3)
10.2 Some distorted polygon flexagons
140(9)
10.3 Right angle triangle flexagons
149(5)
11 Flexahedra 154(10)
11.1 Four dimensions
154(1)
11.2 Prism flexahedra
155(2)
11.3 Pyramid flexahedra
157(1)
11.4 Cube flexahedra
158(6)
References 164(3)
Flexagon index 167(2)
Subject index 169

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