The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace Your ShoesAmerican Mathematical Soc., 2006/05/23 - 125 ページ 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. |
目次
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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多く使われている語句
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 prove pulley sum reduced lacing reef knot result 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 superstraight n-lacings top horizontal traveling salesman problem Venn diagram vertical direction vertical mirror image vertical/diagonal sequence