You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:


Log in to your personal account or through your institution.

Roads and Wheels, Roulettes and Pedals

Fred Kuczmarski
The American Mathematical Monthly
Vol. 118, No. 6 (June‒July 2011), pp. 479-496
DOI: 10.4169/amer.math.monthly.118.06.479
Stable URL:
Page Count: 18
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Item Type
Roads and Wheels, Roulettes and Pedals
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.

Page Thumbnails