Mathematical Recreations; July 1996; Scientific American Magazine; by Stewart; 3 Page(s)

Who is a mathematician? Some years ago, in a rare flash of insight, it dawned on me that a mathematician is somebody who sees an opportunity for doing mathematics where others might not. Consider shoelaces. The potential for extracting significant mathematics from shoelaces is not widely recognized. That it exists was made clear to me by the article "The Shoelace Problem," by John H. Halton, who is in the computer science department of the University of North Carolina at Chapel Hill. It appeared in the Fall 1995 issue of the Mathematical Intelligencer.

There are at least three common ways to lace shoes [see illustration below]: American zigzag, European straight (from which the term "straitlaced" is derived, though perhaps by way of garments rather than shoes) and quick-action shoe store. To the purchaser, styles of lacing can differ in their aesthetic appeal and in the time required to tie them. To the shoe manufacturer, a more pertinent concern is which type of lacing requires the shortest--and therefore cheapest-- laces. In this month¿s column I shall ask the shoe manufacturer¿s question.