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8

Just wanted to update everyone that things are much simpler, - there is built in support for this: MeshFunctions -> {"ArcLength"} So for our case: Show[{ ParametricPlot3D[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi}, (* the trick *) Mesh -> 15, MeshFunctions -> {"ArcLength"}, (* styles *) MeshStyle -> Directive[Red, ...


3

I would localize the variables inside the DynamicModule created by the Manipulate by using the ControlType -> None (or simply None for short) specification. This use is discussed here: What does None mean in a control specification for Manipulate? ControlType -> None Vs. Module inside Manipulate (i.e. making everything local) Code: ...


1

As stated in the OP Mathematica finds this value of the integral within seconds f0 = Integrate[x^2 Log[1 - E^-x], {x, 0, \[Infinity]}] (* Out[21]= -(\[Pi]^4/45) *) Most probably Mathematica employs this standard procedure: 1) solve the indefinte integral, i.e. find an antiderivative 2) check continuity of the antiderivative 3) use the fundamental ...



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