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.
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"... 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
"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
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.
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2 of 2 people found the following review helpful:
5.0 out of 5 stars
A Mathematical Exploration of Tying One's Shoes,
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This review is from: The Shoelace Book: A Mathematical Guide to the Best (And Worst) Ways to Lace Your Shoes (Mathematical World) (Paperback)
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.
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Inside This Book
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First Sentence:
We start by describing the simple models of shoes and lacings of shoes that we will be working with in the following. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
longest vertical length, shortest lacings, linear shoes, longest dense, classical shoe, middle eyelet, zigzag lacings, shortening rules, shoelace problem, vertical mirror image, lengthening rule, such lacings, lace your shoes, two eyelets, long shoes, short shoes, reduced configurations, second endpoint, vertical lengths, real shoes New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We start by describing the simple models of shoes and lacings of shoes that we will be working with in the following. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
longest vertical length, shortest lacings, linear shoes, longest dense, classical shoe, middle eyelet, zigzag lacings, shortening rules, shoelace problem, vertical mirror image, lengthening rule, such lacings, lace your shoes, two eyelets, long shoes, short shoes, reduced configurations, second endpoint, vertical lengths, real shoes New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 3
books:
- Handmade Shoes for Men by Magda Molnar in Back Matter
- The Encyclopedia of Integer Sequences by N. J.A. Sloane in Back Matter
- Loose Lace! by Random House in Back Matter
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