Trochoid

A cycloid (a common trochoid) generated by a rolling circle

In geometry, a trochoid (from Greek trochos 'wheel') is a roulette curve formed by a circle rolling along a line. It is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line.[1] If the point is on the circle, the trochoid is called common (also known as a cycloid); if the point is inside the circle, the trochoid is curtate; and if the point is outside the circle, the trochoid is prolate. The word "trochoid" was coined by Gilles de Roberval, referring to the special case of a cycloid.[2]

  1. ^ Weisstein, Eric W. "Trochoid". MathWorld.
  2. ^ Whitman, E. A. (1943). "Some historical notes on the cycloid". American Mathematical Monthly. 50 (5): 309–315. doi:10.1080/00029890.1943.11991383. JSTOR 2302830.