The shoelace book : a mathematical guide to the best (and worst) ways to lace your shoes / Burkard Polster.

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Bibliographic Details
Uniform Title:Mathematical world ; v. 24.
Main Author: Polster, Burkard
Language:English
Published: Providence, R.I. : American Mathematical Society, [2006], ©2006.
Series:Mathematical world ; v. 24.
Subjects:
Mathematics > Miscellanea.
Combinatorial optimization.
Shoelaces > Mathematics.
Mathématiques > Miscellanées.
Optimisation combinatoire.
Lacets > Mathématiques.
Genre:
Miscellanea.
Miscellanées.
Physical Description:x, 125 pages : illustrations ; 26 cm.
Format: Book
Contents:
  • Preface
  • 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-lacings
  • 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.3. Questions of style
  • 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.