Dissections Plane and Fancy

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

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.

This is a comprehensive, beautifully illustrated survey about puzzles in which one geometric figure is cut into pieces that rearrange to form another. The author explains solution methods carefully, assuming only a basic knowledge of high school geometry, and gives historical background on the puzzles and their originators.