Synopses & Reviews
Can you cut an octagon into five 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. Through the ages, geometric dissections have fascinated puzzle fans and great mathematicians alike. Here are dissections known to Plato and exciting new discoveries alike. Greg Frederickson explains solution methods carefully, assuming only a basic knowledge of high school geometry. This beautifully illustrated book provides hours of enjoyment for every mathematical puzzle enthusiast.
Review
"This book promises to serve as the bible of recreational dissections for at least a generation, just as Harry Lindgren's Recreational Problems in Geometric Dissections and How to Solve Them was the classic source from 1964 to the present. It is clear by browsing through the book and the web page that the field of recreational dissections is alive and well. Frederickson's book will lead it well into the next century." MAA Online"This is a much awaited sequel to Harry Lindgren's 1964 classic work, Geometric Dissections, which the author [Frederickson] revised and augmented in the 1972 Dover edition. Actually, the current volume is much more than just a sequel. It is the most comprehensive treatise on the subject of geometric dissections...[T]his book is a collection of interesting dissection puzzles, old and new...This book is an instructive manual on the art and science of geometric dissections...Finally, this book is an important historical document, detailing the inter-cultural development of the subject...In conclusion, the reviewer echoes Martin Gardner that this book will be a classic. It comes with the highest recommendation." Crux Mathematicorum with Mathematical Mayhem"A wonderfully entertaining book..." Scientific American"...brings the field up to date with recent discoveries, and like its predecessor is beautifully illustrated, but the new volume makes much more interesting reading, full of history, literary pastiches, biographies of nearly 50 contributors to the field of dissections, and Frederickson's accounts of his own discoveries, and how he came to make them. A nine-page biography and two indexes are included. This is an essential book for anyone with interest in geometric dissections." World Game Review"A beautiful book that entices, entertains, fascinates, and instructs. Collects, organizes, and presents 2000+ years of discovery alongside exciting new contributions. Complete, thorough, fun to read; this will be a classic." American Mathematical Monthly"In this book, you will find some of the most challenging of dissection type puzzles, sure to keep you interested from the opening slice to the final splice." Journal of Recreational Mathematics"...a comprehensive survey of dissection problems in elementary geometry...beautifully illustrated." Mathematical Reviews"beautiful and wittily presented...The book can be enjoyed at many levels." SIAM Review
Review
"A beautiful book that entices, entertains, fascinates, and instructs. Collects, organizes, and presents 2000+ years of discovery alongside exciting new contributions. Complete, thorough, fun to read; this will be a classic." - American Mathematical Monthly
Synopsis
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.
Table of Contents
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.