KnotData not working right
- To: mathgroup at smc.vnet.net
- Subject: [mg128344] KnotData not working right
- From: Roger Bagula <roger.bagula at gmail.com>
- Date: Mon, 8 Oct 2012 02:32:44 -0400 (EDT)
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- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
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I did this with torus knots and got a spectrum of results but using the built in KnotData[] I only get one result that is much higher: a = KnotData[All] (* knot definition*) w = {x, y, z} = KnotData[a[[n]], "SpaceCurve"][t] (* Gaussian curvature definition for the curve*) r[t_] = w mag[v_] := Sqrt[v[[1]]^2 + v[[2]]^2 + v[[3]]^2] w2 = Cross[r'[t], r''[t]] k[t_] = Cross[r'[t], r''[t]]/mag[r'[t]]^3 (* calculation of surface Integral of Gaussian curvature by the \ Gauss-Bonnet theorem*) (*http://en.wikipedia.org/wiki/Gauss% E2 %80 \ %93 Bonnet_theorem*) Table[ NIntegrate[Sum[k[t][[i]], {i, 1, Length[k[t]]}], {t, 0, 2*Pi}], {n, 1, Length[a]}] Table[p /. Solve[NIntegrate[ Sum[k[t][[i]], {i, 1, Length[k[t]]}], {t, 0, 2*Pi}] - 2*Pi (2 - 2*p) == 0, p], {n, 1, Length[a]}] ListLinePlot[%]