Hinged Dissections: Swinging and Twisting

✍ Scribed by Greg N. Frederickson

• Publisher: Cambridge University Press
• Year: 2002
• Tongue: English
• Leaves: 303
• Edition: 1
• Category: Library

✦ Synopsis

If you enjoy beautiful geometry and relish the challenge and excitement of something new, the mathematical art of hinged dissections is for you. Using this book, you can explore ways to create hinged collections of pieces that swing together to form a figure. Swing them another way and then, like magic, they form another figure! The profuse illustrations and lively text will show you how to find a wealth of hinged dissections for all kinds of polygons, stars and crosses, curved and even three-dimensional figures. The author includes careful explanation of ingenious new techniques, as well as puzzles and solutions for readers of all mathematical levels. These novel and original dissections will be a gold mine for math puzzle enthusiasts, for math educators in search of enrichment topics, and for anyone who loves to see beautiful objects in motion.

✦ Table of Contents

Cover......Page 1
About......Page 3
Hinged Dissections: Swinging & Twisting......Page 5
Copyright - ISBN: 0521811929......Page 6
Contents......Page 9
Preface......Page 11
1. If it Ain't got that Swing......Page 15
The Curious Case of the Brass Hinges......Page 22
2. Hinging on the Details......Page 25
3. Tricks for Turning......Page 32
Turnabout 1: Coloring a Hinged Model......Page 45
4. Making Squares Dance......Page 47
5. L'Affaire Triangulaire......Page 62
Curious Case, part 2: Five Easy Pieces?......Page 69
6. Return to Polygonia......Page 71
7. Who's the Squarest of Them All?......Page 79
Turnabout 2: Bracing Regular Polygons......Page 84
8. Stepping Around......Page 86
9. All in the Family......Page 92
Curious Case, part 3: Trouble with Attributions......Page 104
10. Elation in Tessellations......Page 107
11. Strips Revealed......Page 115
Turnabout 3: Hinged Tesselations......Page 131
12. With a little Help from my Friends......Page 133
13. At Cross Purposes......Page 140
Curious Case, part 4: A Dudeneyan Slip?......Page 145
14. Handling the Curves......Page 148
15. And Also Starring......Page 153
Turnabout 4: Hinge-Convertible Polyominoes......Page 165
16. Four of a Kind......Page 168
17. As the Whirled Turns......Page 174
Curious Case, part 5: A Quorum of Quibbles......Page 189
18. A New Breed of Swingers......Page 191
19. Not your Regular Polygons......Page 206
Turnabout 5: Piano-Hinged Polyhedra......Page 209
20. Into Another Dimension......Page 212
21. The Flip Side......Page 224
Curious Case, part 6: Statistically Piquing......Page 240
22. Twist and Shout!......Page 242
23. Puzzles Unhinged......Page 272
Afterword......Page 283
Bibliography......Page 287
Index of Dissections......Page 295
General Index......Page 299