Date: Jun 14, 2009 1:31 PM
Author: David W. Cantrell
Subject: Re: A single term formula for calculating the circumference of ellipse

Shahram Zafary <> wrote:
> Hello dear Mr. Cantrell.
> Thanks a lot, for your really exact comments on my formula.
> I am really grateful and hope you permit me contact you again about this
> formula and some same findings that I found out before

Dear Mr. Zafary,

You are certainly welcome to contact me using my 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


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!

Best regards,