The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your ShoesCrisscross, 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. |
Contents
OneColumn Lacings | 7 |
Counting Lacings | 19 |
The Shortest Lacings | 29 |
Variations on the Shortest Lacing Problem | 47 |
The Longest Lacings | 59 |
The Strongest Lacings | 83 |
The Weakest Lacings | 101 |
A Related Mathematics | 107 |
| 121 | |
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Common terms and phrases
1-diagonals 1-verticals angel n-lacings bijective function bowtie n-lacings chapter classes of n-lacings classical shoe conclude configuration correspond crisscross n-lacing dense lacing dense-and-simple n-lacings diagonal diagram in Figure different classes ending in eyelet equal equation exactly exploded n-contraction exploded zigzag n-lacing eyelet A1 function granny knot implies integers Lemma linear shoes long shoes longest n-lacings longest one-column n-lacings longest vertical length loop mathematical shoe maximal length middle eyelet n-lacing contains n-lacings for short n-lacings of longest n-lacings that contain n-lacings that contract n-shoe nonhorizontal segments number of verticals open n-lacings oriented n-lacings possible number proof of Theorem properties pulley sum reduced lacing reef knot segments ending short shoes shortening rules shortest dense n-lacing shortest n-lacings shortest straight n-lacings simple exploded n-lacing simple n-lacings soft straight n-lacing split n-partition star n-lacings strongest n-lacings superstraight n-lacings top horizontal traveling salesman problem Venn diagram vertical direction vertical mirror image vertical/diagonal sequence