Published online 5 December 2002 | Nature | doi:10.1038/news021202-4

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# Laces high

Of the millions of ways to tie our shoes, we've chosen the best.

Shoes change, but lacings never do.© GettyImages

We commonly use only two of the millions of ways to lace a shoe, because they are the best balance of strength and efficiency, finds new research1.

"Hundreds of years of trial and error have led to the strongest way of lacing our shoes," says mathematician Burkard Polster: the 'straight-lace' and 'criss-cross' methods. But there are about 400 million different "reasonable" ways of weaving one lace through a shoe with seven eyelets down each side, says Polster, who works at Monash University in Victoria, Australia.

The most efficient method is the 'bow tie' - occasionally used in shoe shops displays. It takes up all of a shoe's eyelets, but the least amount of lace. The strongest lacing methods - those that give the maximum horizontal tension on both sides of a shoe - are the tried and trusted straight or criss-cross approaches.

Polster's 40-page mathematical investigation of lacing reveals that strange things can happen even in such a simple system. For instance, relative to the amount of lace used, the criss-cross approach is slightly stronger than straight lacing when eyelets are close together. If they are further apart, straight lacing wins.

The difference is quite small. "I don't expect Nike to go out and change the lacings on all their shoes," says Polster. But the fact that the lacing doesn't change with fashions suggests these subtleties are important. "Shoes change like crazy but lacings never do," he says.

The way we fasten the bows on our shoes comes nowhere close to the mathematical purity of lacing, however. Granny knots, double or not, are "notoriously unstable" compared to reef knots for tying laces, says Polster. He suggests swapping the orientation of the second half-knot when tying the bow; this makes a reef knot.

• ## References

1. Polster, B. What is the best way to lace your shoes?. Nature, 420, 476, (2002). | Article | ISI | ChemPort |

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