Curvature for a circle

• To: mathgroup at smc.vnet.net
• Subject: [mg83082] Curvature for a circle
• From: dpdoughe at dialup4less.com
• Date: Sat, 10 Nov 2007 03:38:39 -0500 (EST)

```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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