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The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your Shoes
Burkard Polster, Monash University, Clayton, Victoria, Australia

Mathematical World
2006; 125 pp; softcover
Volume: 24
ISBN-10: 0-8218-3933-0
ISBN-13: 978-0-8218-3933-1
List Price: US$32
Member Price: US$25.60
Order Code: MAWRLD/24
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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.

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.

Want to learn more about knot theory? See The Knot Book by Colin Adams and Knots and Links by Dale Rolfsen.

To read a review published in the Gazette of the Australian Mathematical Society, click here.


General mathematical audience interested in the mathematics of lacing.


"It is more than simply the story of shoelaces and shoes, which is recounted in a fun appendix. It is more a story of mathematics, a story of how when one person stops to ask, 'why do we do things in this way and what is the hidden logic at work,' wonderful things can happen. By boiling a situation down to its essentials, by labeling, measuring, counting, and classifying we set the stage for asking questions whose answers will stretch, surprise, and delight us."

-- PLUS Magazine

"... a very interesting book ... Polster 'ties together' the relevant combinatorial questions in an effective way."

-- Art Benjamin, Harvey Mudd College

"It's a fun book ... interesting and it'll have a wide audience"

-- Fernando Gouvea, Colby College

"... well thought out and well presented."

-- Ian Stewart, University of Warwick

"The analyses are elegant, simple, and should be accessible to a reader with a basic understanding of calculus. The book has a formal mathematical layout, and is very readable. Beyond that, it must be mentioned that it is beautiful!"

-- Gazette of the Australian Mathematical Society

"This clearly written book with many helpful illustrations uses combinatorics and elementary calculus in a series of theorems, lemmas, and proofs. Some proofs are left as exercises for the reader. The book seems most appropriate for upperlevel undergraduate mathematics students but could be used to create an enrichment project for a talented high school student."

-- Mathematics Teacher

"A very enjoyable book indeed."

-- European Mathematical Society Newsletter

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