The Shoelace Book: A Mathematical Guide to the Best (And Worst) Ways to Lace Your Shoes (Mathematical World) (Paperback)

by Burkard Polster (Author) "We start by describing the simple models of shoes and lacings of shoes that we will be working with in the following..." (more)
Key Phrases: longest vertical length, shortest lacings, linear shoes (more...)

Editorial Reviews

Product Description
Crisscross, zigzag, bowtie, devil, angel, or star: which are the longest, the shortest, the strongest, and the weakest lacings? Pondering the mathematics of shoelaces, the author paints a vivid picture of the simple, beautiful, and surprising characterizations of the most common shoelace patterns. The mathematics involved is an attractive mix of combinatorics and elementary calculus. This book will be enjoyed by mathematically minded people for as long as there are shoes to lace.

About the Author
Burkard Polster is a well-known mathematical juggler, magician, origami expert, bubble-master, shoelace charmer, and "Count von Count" impersonator. His previous books include A Geometrical Picture Book, The Mathematics of Juggling, and QED: Beauty in Mathematical Proof.

Product Details

• Paperback: 125 pages
• Publisher: American Mathematical Society (June 3, 2006)
• Language: English
• ISBN-10: 0821839330
• ISBN-13: 978-0821839331
• Product Dimensions: 9.8 x 6.4 x 0.3 inches
• Shipping Weight: 8 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
• Amazon.com Sales Rank: #952,320 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars A Mathematical Exploration of Tying One's Shoes, December 31, 2007

By	D. S. Bakin (Seattle, WA United States) - See all my reviews (REAL NAME)

This book is a fun exploration of "shoelace mathematics". The author first classifies various lacing patterns according to various criteria, and then derives formulas and proofs answering questions like "What are the shortest laces you need to lace a shoe, and what pattern do you lace it in" and "What is the strongest lacing pattern".

The book has fairly simple prerequisites: it uses algebra, uses the combinatorial formula and series of sums, and, in the section on the strongest lacings, some calculus. Most of the math can be understood by working it out on paper, but there are some questions that might occur to the reader that a graphing calculator might be useful for. Or a program like Microsoft Math.

The best part of the book is the attitude it teaches: You do mathematics by starting with a very simple question like "What is the shortest way to lace a pair of shoes" and investigate it, then go on to other questions that occur to you, and on and on, until you're answering all kinds of related questions. It is an exploration. It also teaches how you can do this: You start by breaking off smaller problems that you can answer, using models that are simpler than what you're after, and after searching for and finding solutions to the simpler problem you can start answering related questions, and then more difficult questions. There are plenty of shoelace math questions that might occur to the reader that he could go on to investigate on his own.

The book also shows that mathematics needn't be totally dry. It entertains with photos of real shoes laced in various ways, has some Peanuts and Dilbert and other cartoons, discusses related problems (like the Traveling Salesman problem), and even some history of shoelacing.

The author also wrote a book on the mathematics of juggling, called (of course) "The Mathematics of Juggling". That is also a terrific book showing how you can investigate the mathematics of a problem - I think it is more difficult mathematics, however.