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.... > >