If 
and 
are two points on an ellipse
 |
(1)
|
with eccentric angles 
and 
such that
 |
(2)
|
and 
and 
.
Then
 |
(3)
|
This follows from the identity
 |
(4)
|
where 
is an incomplete elliptic integral
of the second kind, 
is a complete elliptic
integral of the second kind, and 
is a Jacobi
elliptic function. If 
and 
coincide, the point where they coincide is called Fagnano's
point.
