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Re: Curvature for a circle
*To*: mathgroup at smc.vnet.net
*Subject*: [mg83115] Re: Curvature for a circle
*From*: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>
*Date*: Sun, 11 Nov 2007 03:02:20 -0500 (EST)
*References*: <fh3qqc$o9$1@smc.vnet.net>
This looks like a homework question, so I will limit my response to hints:
Have a look at the Wikipedia page on curvature at
http://en.wikipedia.org/wiki/Curvature, where you will see an expression for
curvature \[Kappa] in the plane defined in terms of (derivatives) of y[x].
The rest is up to you to do.
--
Steve Luttrell
West Malvern, UK
<dpdoughe at dialup4less.com> wrote in message news:fh3qqc$o9$1 at smc.vnet.net...
> It can easily be shown that the curvature for a circle of radius r is
> 1/r. How can I get Mathematica to show me this?
>
> I have defined a function to calculate the curvature for me assuming a
> vector-valued function.
>
> Curvature =
> Function[{V, x}, Norm[D[D[V, x]/Norm[D[V, x]], x]/Norm[D[V, x]]]];
>
> S = {2*Cos[theta], 2*Sin[theta]}
>
> ListPlot[Table[{t, Curvature[S, theta] /. theta -> t}, {t, 0, 2*Pi}]]
>
> I don't get anything for a plot. If I look at what my curvature
> formula calculates for me there are some questions as to if
> Abs' (Derivative of absolute value??) being left unevaluated.
>
> Any thoughts? It should be a straight-forward calculation....
>
>
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