Tying Shoes: Math May Make Case for How We Lace

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"The interest of all work in this area lies in the methods and the use of a simple example to illuminate general principles," Stewart said. "We learn nothing of practical value about shoelaces that couldn't be found by experiment—but we learn some interesting things about how to tackle other problems of a similar kind, and those are often of practical value."

All Tied Up In Knots

Using the most efficient lacing technique is only half the battle; then there's what kind of knot to tie.

"Hundreds of years of trial and error have led to the strongest way of lacing our shoes," said Polster. "Unfortunately, the same cannot be said about the way in which most of us tie our shoelaces."

The problem, he said, is that many people use a "granny knot," which they form by passing first one end of the lace around the other and then the second around the first from the same angle. This forms two identical half-knots on top of each other.

Better than the granny knot, Polster said, is the reef knot, which is commonly used by sailors. The reef knot, also called a square knot, is similar to the granny knot except that its two half-knots are oriented in opposite directions. [ Need a diagram? ]

The bows that people make while tying shoelaces have nothing to do with making the knot stronger, and serve only to make the knot easier to untie. They can be ignored for the purpose of comparing different knots.

"I have a better way of tying shoes," said John H. Halton, a professor of computer science at the University of North Carolina at Chapel Hill whose earlier paper on the subject inspired Polster's latest work.

Halton, now 71, learned a memorable trick decades ago, when he was a student at Oxford University. His instructor for the lesson was no luminary of academia; just a salesman at a local shoe store, who patiently demonstrated to a curious Halton how to tie laces with a surgeon's knot.

That knot resembles a reef knot, but includes one extra loop: "The rabbit goes back down the hole and comes up again," as Halton put it. Halton swears by the surgeon's knot and has been using it ever since he learned it. He's even taught the trick to friends and relatives who will humor him. Despite his efforts, he laments, "it simply has not caught on."

"Some people teach Christianity or Islam; I teach shoe tying," jokes the computer science prof. That, and, oh yeah, perhaps a few university-level computation problems that would make the average mortal's brain go numb.

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