A cranioid is a curve whose name means skull-like. It is given by the polar equation
 |
where 
, 
, 
, 
, and 
. The top of the curve corresponds to ![t in [0,pi]](/images/equations/Cranioid/Inline6.svg)
, while the bottom corresponds to ![t in [pi,2pi]](/images/equations/Cranioid/Inline7.svg)
.
It has area given by
![A=1/2pi[a^2-b^2(p-2)-c^2(q-2)+4bcF_1(1/2;-1/2,-1/2;1;p,q)],](/images/equations/Cranioid/NumberedEquation2.svg) |
where 
is an Appell
hypergeometric function.
