Let S be the set of all points in the plane that can be expressed in the form (\cos a + \cos b, \sin a + \sin b) where a and b are real numbers. Find the area of the set S

You get some nice curves with x = cos(a) + cos(b); y = sin(a) + sin(b).

Presumably, with an infinite number of points the area covered is that of a circle with radius 2.

Area = 4pi.