Softcover ISBN:  9780821839331 
Product Code:  MAWRLD/24 
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eBook ISBN:  9781470418106 
Product Code:  MAWRLD/24.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9780821839331 
eBook: ISBN:  9781470418106 
Product Code:  MAWRLD/24.B 
List Price:  $94.00 $71.50 
MAA Member Price:  $84.60 $64.35 
AMS Member Price:  $75.20 $57.20 
Softcover ISBN:  9780821839331 
Product Code:  MAWRLD/24 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
eBook ISBN:  9781470418106 
Product Code:  MAWRLD/24.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9780821839331 
eBook ISBN:  9781470418106 
Product Code:  MAWRLD/24.B 
List Price:  $94.00 $71.50 
MAA Member Price:  $84.60 $64.35 
AMS Member Price:  $75.20 $57.20 

Book DetailsMathematical WorldVolume: 24; 2006; 125 ppMSC: Primary 00; 90; 05
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 wellknown mathematical juggler, magician, origami expert, bubblemaster, 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 .
ReadershipGeneral mathematical audience interested in the mathematics of lacing.

Table of Contents

Chapters

1. Setting the stage

2. Onecolumn lacings

3. Counting lacings

4. The shortest lacings

5. Variations on the shortest lacing problem

6. The longest lacings

7. The strongest lacings

8. The weakest lacings

A. Related mathematics

B. Loose ends


Additional Material

Reviews

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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 Book Details
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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 wellknown mathematical juggler, magician, origami expert, bubblemaster, 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.

Chapters

1. Setting the stage

2. Onecolumn lacings

3. Counting lacings

4. The shortest lacings

5. Variations on the shortest lacing problem

6. The longest lacings

7. The strongest lacings

8. The weakest lacings

A. Related mathematics

B. Loose ends

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