You are certainly welcome to contact me using my sigmaxi.net email address.

I mentioned your nice formula to Gerard Michon recently, and he has now
added a section about it on his Numericana site. See

<www.numericana.com/answer/ellipse.htm#zafary>.

Note that Gerard found a very nice alternative way of writing your
approximation: The quantity h = ((a - b)/(a + b))^2 often appears in
dealing with the perimeter of an ellipse. Using h, your approximation can
be written simply as

pi (a + b) (4/pi)^h

Although I really liked your approximation before, I like it even more in
the form above!