**Mathematical World**

Volume: 24;
2006;
125 pp;
Softcover

MSC: Primary 00; 90; 05;

Print ISBN: 978-0-8218-3933-1

Product Code: MAWRLD/24

List Price: $34.00

AMS Member Price: $27.20

MAA Member Price: $30.60

**Electronic ISBN: 978-1-4704-1810-6
Product Code: MAWRLD/24.E**

List Price: $32.00

AMS Member Price: $25.60

MAA Member Price: $28.80

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#### Supplemental Materials

# The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your Shoes

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*Burkard Polster*

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

#### Readership

General mathematical audience interested in the mathematics of lacing.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your Shoes

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface vii8 free
- Setting the stage 112 free
- One-column lacings 718
- Counting lacings 1930
- The shortest lacings 2940
- Variations on the shortest lacing problem 4758
- The longest lacings 5970
- The strongest lacings 8394
- The weakest lacings 101112
- Related mathematics 107118
- Loose ends 111122
- References 121132
- Index 123134 free
- Back Cover Back Cover1138