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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.
A small knot. The small knot, also known as oriental knot, Kent knot, or simple knot, is the simplest method of tying a necktie. Unlike the Four-in-hand knot and Windsor knot, the small knot is not self-releasing. The small knot is tied inside out, though this can be mitigated by giving the tie a half-twist during the tying process.
Like the Pratt knot, it is tied inside-out. It originated in Milan, Italy and may have been named after Nikita Khrushchev after he visited the city. The knot is larger than the Four-in-hand knot and smaller than the Half-Windsor knot. [2] Using the notation of The 85 Ways to Tie a Tie, the Nicky knot is tied Lo Ci Ro Li Co T (knot 4).
Hitching tie – simple knot used to tie off drawstring bags that allows quick access; Honda knot a.k.a. lariat loop – loop knot commonly used in a lasso; Hoxton knot – a method of arranging a scarf about the neck; Hunter's bend a.k.a. rigger's bend – joins two lines
The Pratt knot uses less length than the half-Windsor or Windsor knots, and so is well suited to shorter ties or taller men. Unlike the four-in-hand knot, the Pratt method produces a symmetrical knot. It is of medium thickness. Using notation from and according to The 85 Ways to Tie a Tie, the knot is tied Lo Ci Lo Ri Co T (knot 5).
The Grantchester knot is a self-releasing, asymmetric way of tying a necktie. Using the notation presented in The 85 Ways to Tie a Tie , it is a Lo Ri Lo Ri Co Li, finishing with Ro Li Co T. Grantchester knot instructions
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The diamond knot (or knife lanyard knot) is a knot for forming a decorative loop on the end of a cord such as on a lanyard. [1] A similar knot, also called the diamond knot, is a multistrand stopper knot, that is similar in appearance (although the footrope knot is really more similar, but it is simply an upside down diamond knot).