Jon O'Lobster (Jonolobster)
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Tie Knots

During their time at Cambridge University’s Cavendish Laboratory, Anglo-American Physicist Thomas Fink and his colleague Yong Mao learnt how to tie ties.

Seeking a marriage of science and beauty, Thomas M. A. Fink and Yong Mao, research fellows at Cambridge University, have applied the rigors of mathematics to that most basic of fashion statements, the necktie knot. In the process they have come up with six new ways of tying a tie.

Dr. Fink, who in his more serious moments investigates protein folding, and Dr. Mao, who specializes in colloids and polymers, felt that the world might be ready for a new knot or two. Of the four in common use, the four-in-hand (so named because it was used by drivers of four-in-hand carriages) dates from the 19th century, while the Windsor and the half-Windsor, were popularized in the 1930's by the Duke of Windsor. Only the Pratt knot, publicized about a decade ago, has a more recent history, and some dismiss it as simply a reverse Windsor.

More here (article): https://goo.gl/TKEHYR

Of the 85 possible tie knots that can be tied with a tie of conventional length, the following are of particular interest. The first number is the number of the knot, as catalogued in the Summary of Knots in The 85 Ways and at the bottom of this page. Some of the knots have close cousins with which they are often confused (not including mirror images). These typically involve the transposition of one or more L-R pairs. They are indicated by prefixing the name of their relation with 'co-', as in co-Windsor.

More here (blog): https://goo.gl/ahS7N7

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. Thus enumerating tie knots of n moves is equivalent to enumerating walks of n steps. Imposing the conditions of symmetry and balance reduces the 85 knots to 13 aesthetic ones.

The 85 Ways to Tie a Tie (Wikip): https://goo.gl/Pr3y4Y

The 85 Ways to Tie a Tie (Library): https://goo.gl/vz8SCm

Designing tie knots by random walks (Nature pdf): https://goo.gl/IFXr0z

Tie knots, random walks and topology (Nature pdf): https://goo.gl/pnHcZW

Image: https://goo.gl/HBxrJe﻿
Post has shared content
Tie Knots

During their time at Cambridge University’s Cavendish Laboratory, Anglo-American Physicist Thomas Fink and his colleague Yong Mao learnt how to tie ties.

Seeking a marriage of science and beauty, Thomas M. A. Fink and Yong Mao, research fellows at Cambridge University, have applied the rigors of mathematics to that most basic of fashion statements, the necktie knot. In the process they have come up with six new ways of tying a tie.

Dr. Fink, who in his more serious moments investigates protein folding, and Dr. Mao, who specializes in colloids and polymers, felt that the world might be ready for a new knot or two. Of the four in common use, the four-in-hand (so named because it was used by drivers of four-in-hand carriages) dates from the 19th century, while the Windsor and the half-Windsor, were popularized in the 1930's by the Duke of Windsor. Only the Pratt knot, publicized about a decade ago, has a more recent history, and some dismiss it as simply a reverse Windsor.

More here (article): https://goo.gl/TKEHYR

Of the 85 possible tie knots that can be tied with a tie of conventional length, the following are of particular interest. The first number is the number of the knot, as catalogued in the Summary of Knots in The 85 Ways and at the bottom of this page. Some of the knots have close cousins with which they are often confused (not including mirror images). These typically involve the transposition of one or more L-R pairs. They are indicated by prefixing the name of their relation with 'co-', as in co-Windsor.

More here (blog): https://goo.gl/ahS7N7

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. Thus enumerating tie knots of n moves is equivalent to enumerating walks of n steps. Imposing the conditions of symmetry and balance reduces the 85 knots to 13 aesthetic ones.

The 85 Ways to Tie a Tie (Wikip): https://goo.gl/Pr3y4Y

The 85 Ways to Tie a Tie (Library): https://goo.gl/vz8SCm

Designing tie knots by random walks (Nature pdf): https://goo.gl/IFXr0z

Tie knots, random walks and topology (Nature pdf): https://goo.gl/pnHcZW

Image: https://goo.gl/HBxrJe﻿