In my enthusiasm I forgot to send this to the list as well as Frans!
-------------Forwarded Message-----------------
From: Patrick Powers,
To: "Frans W. MAES", INTERNET:[EMAIL PROTECTED]
Date: 16/03/2001 14:40 PM
RE: Circumference of ellipse
Message text written by "Frans W. MAES"
>...does anyone of you happen to know of a NON-
mathematical, intuitively convincing explanation for the fact that
there is no 'simple' formula for the circumference of an ellipse?<
Not sure that I do though I had always assumed it was because the equations
you encounter in the process of doing the calculation turn out to be
transcendental (like you get when trying to solve Kepler's Equation for
elliptical motion E=M+esinE) and therefore cannot be solved directly. With
transcendental equations you cannot simply rearrange the terms to find the
parameter you want..
Several approximations exist, Ramanujan's (1914) is:
L=PI(3*(a+b)-SQRT((a+3b)*(3a+b)))
Where the ellipse is ( x*x/a*a ) +( y*y/b*b) =1and a is the semi-major axis
and b the semi minor one.
Patrick
