Tying Shoes: Math May Make Case for How We Lace

Ben Harder
for National Geographic News
December 4, 2002

Math-phobes of the world, take heart! You might not have realized it, but you've been acing at least one math problem each morning since the day you gave up Velcro.

The way most people tie their shoes is, in fact, the most effective way to secure footwear to feet, according to mathematician Burkard Polster.

There are two basic approaches to lacing up: "criss-cross" lacing—the method most common in North America—or the mainly European style of "straight" lacing, in which laces run parallel above the eyelets and cross below them.

"The strongest lacings turn out to be the two most commonly used ones," said Polster, who teaches at Monash University in Victoria, Australia. "In some unquantifiable way, the common ways of lacing shoes also seem to be the simplest to execute."

"When you pull on the ends of a shoelace," Polster wrote in the December 5 issue of the journal Nature, "it acts like a pulley" that pulls eyelets toward each other, thereby holding the shoe firmly to the foot, and creates tension along the lace. The ideal lacing should create uniform tension along the length of the lace.

Which of the two techniques is stronger depends on the distance between the two rows of eyelets, and therefore, at least in part, on the design of the shoes.

There are methods of lacing that use a shorter length of lace, such as crossing from one row of eyelets to the other only after every second eyelet, said Polster. Shoes laced with this technique would sport a "bow-tie" pattern along their tongues but wouldn't grip the foot as firmly as traditionally laced shoes, he said.

No Fast Break For Footwear

"I don't expect shoe manufacturers to get terribly excited about all this," admitted Polster. "I am really talking about idealized shoes and shoelaces. Things like friction, the material that shoelaces are made of, and less than perfect alignment of eyelets are not taken into account at all."

What would inspire someone to devote time to studying how we tie our shoes?

"Tying shoelaces is a simple, familiar example of a geometrical optimization problem," said Ian Stewart, a professor of mathematics at the University of Warwick in England.

Continued on Next Page >>


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