Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1999
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

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/





  • Prev by Date: Pattern example
  • Next by Date: Re: Gaussian PDF Overlay
  • Previous by thread: circumference of an ellipse
  • Next by thread: Re: circumference of an ellipse