Dissections
Plane and Fancy

A comprehensive, beautifully illustrated survey accessible to anyone familiar with high school geometry.

Greg N. Frederickson (Author)

9780521525824, Cambridge University Press

Paperback, published 3 February 2003

324 pages, 528 b/w illus.
24.4 x 17 x 1.7 cm, 0.52 kg

'Every puzzle fan will like this interesting and amusing book.' EMS Newsletter

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. Through the ages, geometric dissections have fascinated puzzle fans and great mathematicians alike. Here you will find dissections known to Plato alongside exciting new discoveries. 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 - famous, not-so-famous, and obscure - 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, from the 1900 Paris Congress of Mathematicians to the night sky of Canberra. This beautifully illustrated book will provide hours of enjoyment for any mathematical puzzle enthusiast.

1. 'Dat Pussle'
2. Our geometric universe
3. Fearful symmetry
4. It's hip to be a square
5. Triangles and friends
6. All polygons created equal
7. First steps
8. Step right up!
9. Watch your step!
10. Just tessellating
11. Plain out-stripped
12. Strips teased
13. Tessellations completed
14. Maltese crosses
15. Curves ahead
16. Stardom
17. Farewell, my lindgren
18. The new breed
19. When polygons aren't regular
20. On to solids
21. Cubes rationalized
22. Prisms reformed
23. Cheated, bamboozled, and hornswoggled
24. Solutions to all our problems.

Subject Areas: Geometry [PBM]