Dissections: Plane and Fancy

Portada
Cambridge University Press, 3 feb. 2003 - 324 páginas
Can you cut an octagon into 5 pieces and rearrange them into a square? How about turning a star into a pentagon? These are just two of the infinite challenges of geometric dissections, the mathematical art of cutting figures into pieces that can be rearranged to form other figures, using as few pieces as possible. This book shows you many ingenious ways to solve these problems and the beautiful constructions you can create. The author explains solution methods carefully, assuming only a basic knowledge of high school geometry, then poses puzzles for you to solve. He also introduces the people who have worked on these problems, travelling from the palace school of tenth-century Baghdad to the mathematical puzzle columns in turn-of-the-century newspapers. This beautifully illustrated book will provide hours of enjoyment for any mathematical puzzle enthusiast.
 

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Índice

Dat Pussle
1
Our Geometric Universe
10
Fearful Symmetry
20
Its Hip to Be a Square
28
Triangles and Friends
40
All Polygons Created Equal
51
First Steps
60
Step Right Up
71
Curves Ahead
163
Stardom
172
Farewell My Lindgren
187
The New Breed
207
When Polygons Arent Regular
221
On to Solids
230
Cubes Rationalized
247
Prisms Reformed
258

Watch Your Step
89
Just Tessellating
105
Plain OutStripped
117
Strips Teased
136
Tessellations Completed
150
Maltese Crosses
157
Cheated Bamboozled and Hornswoggled
268
Solutions to All Our Problems
278
Bibliography
293
Index of Dissections
303
General Index
307
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