The Shoelace Book: A Mathematical Guide to the Best (And Worst) Ways to Lace Your Shoes (Mathematical World) (Mathematical World, 24)

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. Cover Contents Preface Acknowledgements 1. Setting the Stage 1.1 Popular Lacings 1.2 Dense, Straight, Superstraight, and Simple Lacings 1.3 Notes 2. One-Column Lacings 2.1 The Number of One-Column n-Lacings 2.2 The Shortest One-Column n-Lacings 2.3 The Longest One-Column n-Lacings 2.4 Straight n-Lacings and One-Column n-Lacings 2.5 Notes 3. Counting Lacings 3.1 The Number of n-Lacings 3.2 Notes 4. The Shortest Lacings 4.1 Statement of Results 4.2 The Shortest General and Dense n-Lacings 4.3 The Shortest Straight n-Lacings 4.4 The Shortest Dense-and-Straight n-Lacings 4.5 Comparing the Lengths of Some Popular n-Lacings 4.6 Notes 5. Variations on the Shortest Lacing Problem 5.1 Linear Shoes 5.2 Framed Shoes 5.3 General Shoes 5.4 Open Lacings 5.5 Multi-Loop Lacings 6. The Longest Lacings 6.1 Summary of Results and Conjectures 6.2 The Longest Simple n-Lacings 6.3 The Longest Dense and General n-Lacings 6.4 The Longest Straight and Superstraight n-La 6.5 The n-Lacings of Longest Vertical Length 6.6 Notes 7. The Strongest Lacings 7.1 Statement of Results 7.2 The Strongest n-Lacings 7.3 The Strongest Straight n-Lacings 7.4 Proofs of the Lemmas 7.5 Notes 8. The Weakest Lacings 8.1 Summary of Results and Conjectures 8.2 Notes A. Related Mathematics A.1 Traveling Salesman Problems A.2 The Shoelace Formula B. Loose Ends B.1 History B.2 Shoelace Superstitions B.4 Fashion B.5 What Is the Best Way to Lace Your Shoes? B.6 Foot Problems and Lacings B.7 What Is the Best Way to Tie Your Shoelaces? References Index Back Matter Titles in This Series Families of Lacings Back Cover 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. Table of contents: * Setting the stage * One-column lacings * Counting lacings * The shortest lacings * Variations on the shortest lacing problem * The longest lacings * The strongest lacings * The weakest lacings * Related mathematics * Loose ends (history, shoelace superstitions, questions of style, fashion, what is the best way to lace your shoes, foot problems and lacings, what is the best way to tie your shoelaces?) Crisscross, zigzag, bowtie, devil, angel, or star: which are the longest, the shortest, the strongest, and the weakest lacings? This book presents the mathematics of shoelaces which is a mix of combinatorics and elementary calculus. Burkard Polster. Includes bibliographical references (p. [121]-122) and index.