The cycloid-the curve traced by the path of a fixed point on a circle
which rolls smoothly on a straight line.
<1>the length of arch of the cycloid is four times the diameter
of the revolving circle.
<2>studying the area enclosed under the arch of the cycloid.
the area with a sheet of lead compared it to that of the revolving circle,
and determined the area was three times the area of the circle.
thx