Theory of Tieknots
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|The mathematical theory behind tying a necktie, with illustrations of the Four in Hand, the Pratt Knot, the Half-Windsor, and the Full-Windsor, and a classification of necktie knots with respect to size and shape. Tying a tie knot is equivalent to a persistent random walk on a triangular lattice. Using this model, the number of all possible knots in each class (set by the number of total and centre moves, respectively) is calculated. The optimal knot in each class is determined by the aesthetic conditions of symmetry and balance. Of the 85 tie knots found, the model predicts the four knots in widespread use and introduces nine new ones.|
|Levels:||High School (9-12), College, Research|
|Math Topics:||Order/Lattices, Knot Theory|
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