**What do mathematicians do in their spare time?**

Why, work out the optimum pattern for lacing up shoes. “The knotty problem of choosing the optimum way of lacing up shoes has been solved by a new mathematical proof. The criss-cross and straight patterns are strongest, but the bow-tie pattern is the most efficient The criss-cross and straight patterns are strongest, but the bow-tie pattern is the most efficient

There are many millions of different possibilities but, reassuringly, the proof shows that centuries of human trial and error has already selected out the strongest lacing patterns. However, the pattern using the least amount of lace possible, the decorative “bowtie” lacing, is usually only seen in shoe shop displays.

Burkard Polster, of Monash University in Melbourne, Australia, used combinatorial mathematics to come up with his proof. This branch of maths is used to solve a huge variety of problems, including resource allocation and finding the best ways to lay chips in a computer.

Formulas describing the physics of pulleys were used to work out how much force is exerted on the sides of a shoe using different lacing techniques. The most widely used “criss-cross” and “straight” lacing patterns were identified as the strongest. ”