![Curtate cycloid](/images/gifs/cycloidc.gif)
A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius , where
is the radius of a rolling circle.
Curtate cycloids are used by some violin makers for the back arches of some instruments,
and they resemble those found in some of the great Cremonese instruments of the early
18th century, such as those by Stradivari (Playfair 1999).
A curtate cycloid has parametric equations
(1)
| |||
(2)
|
The arc length from is
(3)
|
where
is an incomplete elliptic integral
of the second kind.