"On the Teeth of Wheels," by Brian Hayes. American Scientist, July/August 2000, pages 296-300.
This article discusses an intriguing connection between number theory and the design of gears. While working on an earlier article about a variant on the well-known Fibonacci numbers, the author came upon a number theory article that had been published in a clockmaker's journal. This led him to investigate the ingenious calculation methods developed by 19th century gear makers. These methods allow one to calculate the number of teeth needed on gears in a gear train to insure that the gears rotate at the correct rate. The computer has made these methods obsolete for gear design, but their value in number theory endures.
--- Allyn Jackson