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....

**Follow-Ups**:**Re: Curvature for a circle***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>