Dissections: Plane and Fancy [Paperback]

Greg N. Frederickson (Author)

Book Description

ISBN-10: 0521525829 | ISBN-13: 978-0521525824 | Publication Date: February 3, 2003

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.

Editorial Reviews

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

Book Description

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.

Product Details

• Paperback: 322 pages
• Publisher: Cambridge University Press (February 3, 2003)
• Language: English
• ISBN-10: 0521525829
• ISBN-13: 978-0521525824
• Product Dimensions: 9.3 x 6.9 x 0.6 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,861,013 in Books (See Top 100 in Books)

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5 of 5 people found the following review helpful:

4.0 out of 5 stars Slicing and splicing for enjoyment, August 1, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Dissections: Plane and Fancy (Hardcover)

Dissections are one area of mathematics where theory usually plays a secondary role to intuition. While the discovery of a solution may take an enormous amount of trial and effort, understanding it is generally a simple verification. For these reasons, dissections can aptly be described as an area of popular mathematics. The puzzles of Sam Loyd were extremely popular, with one even described as having been a national craze in the United States, and some of his most diabolical were dissections. His English counterpart and rival was Henry Dudeney, whose collected works of puzzles also contains many dissections.
As befits the development of abstract geometry centuries ago, the art of dissection goes all the way back to the age of Plato. Starting with a geometric shape and cutting it into pieces that can be rearranged to form another shape is something that clearly is more of a hobby than a career, although it is possible that it may have some applications in space filling.
Art and hobbies aside, this is a fun book to explore. Since the subject matter is the slicing and splicing of geometric figures, most of the results are presented as diagrams, making the solutions easy to understand. One thought constantly leapt to mind when I was examining some of the diagrams, "How did they think of doing that?" Obvious only after the fact, many dissections are hardly something that would easily leap to mind. Additional puzzles are interspersed throughout the text and solutions to all are included at the end of the book.
The public loves puzzles, as the popularity of some game shows and regular puzzle columns in newspapers and magazines demonstrates. 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.

Published in Journal of Recreational Mathematics, reprinted with permission.