You are not currently logged in.
Access JSTOR through your library or other institution:
Roads and Wheels, Roulettes and Pedals
The American Mathematical Monthly
Vol. 118, No. 6 (June‒July 2011), pp. 479-496
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.118.06.479
Page Count: 18
Preview not available
Abstract We revisit the idea of road-wheel pairs, first introduced 50 years ago by Gerson Robison and later popularized by Stan Wagon and his square-wheeled tricycle. We show how to generate such pairs geometrically: the road as a roulette curve and the wheel as a pedal curve. Along the way we gain geometric insight into two theorems proved by Jakob Steiner relating the area and arc length of a roulette to those of a corresponding pedal. Finally, we use our results to generate parabolas, ellipses, and sine curves as roulettes.
Copyright the Mathematical Association of America 2011