Math Forum Discussions

Roger Bagula

Posts: 100
Registered: 7/12/09

KnotData not working right
Posted: Oct 8, 2012 2:52 AM

Plain Text

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[%]