Re: circumference of an ellipse

• To: mathgroup at smc.vnet.net
• Subject: [mg19345] Re: circumference of an ellipse
• From: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>
• Date: Fri, 20 Aug 1999 23:09:30 -0400
• Organization: Defence Evaluation and Research Agency
• References: <7p017c\$778@smc.vnet.net> <7p301g\$anl@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Allan Hayes <hay at haystack.demon.co.uk> wrote in message
news:7p301g\$anl at smc.vnet.net...
> Marcel,
>
> circumference[a_, b_] :=
>   Integrate[Sqrt[D[a Cos[t], t]^2 + D[b Sin[t], t]^2], {t, 0, 2Pi}]
>
>...

(Preamble: I have \$Version = "4.0 for Microsoft Windows (April 21, 1999)")

I agree with this parametric solution, but it exposes a bug in Mathematica
when you evaluate the following symbolic expression:

circumference[a, b]

This gives zero!

Furthermore, if you define

halfcircumference[a_, b_] :=
Integrate[Sqrt[D[a Cos[t], t]^2 + D[b Sin[t], t]^2], {t, 0, Pi}]

and then evaluate halfcircumference[a, b], you get "Infinite expression 1/0
encountered".

Steve Luttrell
Signal Processing and Imagery Department
Malvern, United Kingdom, WR14 3PS

+44 (0)1684 894046 (tel)
+44 (0)1684 894384 (fax)
luttrell at signal.dera.gov.uk (email)

```

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