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MathGroup Archive 1999

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Re: circumference of an ellipse

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19304] Re: circumference of an ellipse
  • From: dennisw555 at aol.com (DennisW555)
  • Date: Sat, 14 Aug 1999 01:45:24 -0400
  • Organization: AOL http://www.aol.com
  • References: <7p017c$778@smc.vnet.net>
  • 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

Here are some results I got

        a=1,  b=1, circ = 6.28318530717958647702
        a= 2, b=1, circ=9.68844822054767619828
        a=4,  b=1, circ=17.1568435503136684457
        a=8,   b=1, circ=32.7449566001955006842
        a=16, b=1, circ=64.4579248618360700975

Hope this helps.  Note, the first is for a circle of radius 1.

Dennis



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