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Close-up of a shoelace knot. The shoelace knot, or bow knot, is commonly used for tying shoelaces and bow ties.. The shoelace knot is a doubly slipped reef knot formed by joining the ends of whatever is being tied with a half hitch, folding each of the exposed ends into a loop and joining the loops with a second half hitch.
Each shoelace typically passes through a series of holes, eyelets, loops or hooks on either side of the shoe. Loosening the lacing allows the shoe to open wide enough for the foot to be inserted or removed. Tightening the lacing and tying off the ends secures the foot firmly within the shoe.
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The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for a lay audience, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end.
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In 2010, Blake Bevin, a self-described "science geek", created a prototype of self-lacing shoes, inspired by Marty's Nike MAG; once the user steps in, a sensor records the pressure of the foot on the sole and activates two servo motors, which apply tension to the laces, thus tightening the shoe.