Problem of the Week 1120

Squaring the Cycloid

A cycloid is the curve generated by a point on a wheel as the wheel rolls. This diagram shows half of a loop of the standard cycloid, whose parametric form is (t - sin t, 1 - cos t):

Which is larger, the blue area or the orange area?

Source: T Apostol and M Mnatsakanian, Amer Math Monthly, Aug-Sept 2009, 598-611.

© Copyright 2009 Stan Wagon. Reproduced with permission.