A
mathematical construct specified by a pair of
parametric equations. Specific case of the more generic
cyclohedron. Related 2D
forms include
hypercycloid and
curtate cycloid, which are also generalizations.
For a cycloid based on a
circle of
radius r with rotation
angle a, the parametric equations are as follows:
x=r(a-sin(a))
y=r(1-cos(a))
An interesting
property of this construct is that the
area under the first
dome-shape (a=0 to a=2
pi) is equal to 8r.