Although scientists are not renowned for their dress sense, two physicists at Cambridge University have put one everyday sartorial task for many men - how to knot a necktie - on a firm mathematical footing. Thomas Fink and Yong Mao have shown that the sequence of steps involved in knotting a necktie can be represented by movements on a triangular lattice. They show that 85 knots can be tied with a conventional tie, and discuss the four most commonly used knots in terms of size, shape, balance and symmetry. They also introduce six new "aesthetically pleasing" knots (Nature 398 31).
In Fink and Mao’s method the space surrounding the tie is split into three sections: left, centre and right. To begin the wide end of the tie is passed either over or under the narrow part. The knotting process then continues with a series of half turns or moves either towards or away from the shirt. By taking “random walks” along the lattice, Fink and Mao devised a mathematical formula for the knots. Although they were able to generate a total of 85 knots with the formula, only 10 were deemed aesthetically pleasing.
