Re: circumference of an ellipse

*To*: mathgroup at smc.vnet.net*Subject*: [mg19300] Re: [mg19299] circumference of an ellipse*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 14 Aug 1999 01:45:22 -0400*Sender*: owner-wri-mathgroup at wolfram.com

>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 >lenght > - 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 >worksheetformulae. >Could someone please give me the exact results (in 10 or 15 digits) of some >examples? >a=2; b=1 >a=5; b=1 >a=100; b=26 > >Thanks in advance! > >Marcel > Marcel, 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 earthlink.net http://home.earthlink.net/~djmp/