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Tie Knots and Random Walks

Thomas M. Fink tex2html_wrap_inline812 and Yong Mao tex2html_wrap_inline814

Theory of Condensed Matter, Cavendish Laboratory, Cambridge, CB3 0HE, UK
tex2html_wrap_inline812 tmf20@cus.cam.ac.uk tex2html_wrap_inline814 ym101@phy.cam.ac.uk

We introduce a mathematical model of tieknots to classify necktie knots with respect to size and shape. It turns out that tying a tie knots is equivalent to a so-called persistent random walks 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, our model duly predicts the four knots in widespread use and further introduces nine new aesthetic ones.





Yong Mao
Aug 7 16:03:57 GMT 1999