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.
Author(s): Burkard Polster
Series: Mathematical World (Book 24)
Publisher: American Mathematical Society
Year: 2006
Language: English
Commentary: Paginated, Outlined, OCR,
Pages: 125
City: Providence, R.I. :
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
