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Re: circumference of an ellipse

  • To: mathgroup at
  • Subject: [mg19300] Re: [mg19299] circumference of an ellipse
  • From: "David Park" <djmp at>
  • Date: Sat, 14 Aug 1999 01:45:22 -0400
  • Sender: owner-wri-mathgroup at

>I made a little spreadsheetfile to calculate the circumference (length) of
>an ellipse using an iterative process.
>When I compare the results with the results of a formula to approximate the
> - which is pi(3(a+b)-sqrt((a+3b)(3a+b))) - the difference is greater then I
>expected (a few percents).
>This may be a shortcoming of the approximation formula, or of my
>Could someone please give me the exact results (in 10 or 15 digits) of some
>a=2; b=1
>a=5; b=1
>a=100; b=26
>Thanks in advance!

These are the results I obtained using a complicated MeijerG function formula which
Mathematica obtained, using a numerical integration of the curve length, and using
your approximate formula.

a        b        MeijerG Function       Numerical Integration    Approximation
2        1        9.68844822054768    9.68844822054768    9.68842109767129
5        1        21.0100445396890    21.0100445396890    21.0056042593493
100     26      430.783975358342    430.783975358342    430.743717219352

David Park
djmp at

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