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I would appreciate any help with this problem:

Find the curvature at (3,0,0) of a torus knot parameterized in 3-space by:

r(t) = [(2+cos2t)cost, (2+cos2t)sint, sin2t].

Obviously, using one of the known curvature formulas--(|VxA| / |V|^3)or |dT|/|ds|--would result in an incredible mess using r(t). It's apparent that t=0 at (3,0,0)--and since the curvature of a circle is 1/radius would the knot be considered a circle of radius 2 at this point? Again--any help would be very appreciated!

Dean

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# Curvature of a torus knot

Can you offer guidance or do you also need help?

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