The Cycloid and the Pendulum Clock

What is a cycloid?

If a point on a wheel is marked and the wheel is rolled on a flat surface, the marked point generates a curve. This curve is called a cycloid. At first, the curve seems ordinary — Galileo suggested that that it would be a nice arc for a bridge — but it has a lot more interesting properties  and uses than that.

The Cycloid Curve

Interesting Properties of a Cycloid

In 1634, Frenchman Gilles Persone de Roberval showed that  the area under one arc of the curve is thrice the area of the generating circle, but did not publish his findings. When Italian Evangelista Toricelli published the same result in 1644, he was accused by the former of plagiarism. Aside from this bitter bickering, numerous conflicts among Geometers were created by the controversial curve, and because of that, it has been called as the “Helen of Geometers.” » Read more