That's interesting. It's the same area as the sum of 3 orthogonal generating circles, the sum of the plan, front and side elevations of a sphere.In 1634 G.P. de Roberval showed that the area under a cycloid is three times the area of its generating circle.
That must have significance - but I'm not quite sure what.
Is there a mathematician in the house?
No?
Thought not.
