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.
© 1996-9 Eric W. Weisstein
1999-05-26