The idea behind my geometry was to create a surface the behaved more like a true Moebius. By that I mean that the surface can be evaluated through the U direction to a position on both sides. See the script.
I chose 4Pi to resemble a circle. With a circle, advancing 2Pi will return you to the start point. With a Mobius, you are at the start point, but on the underside of the surface. 4Pi returns you to the true start point.
Dim domU, domV
srf = .GetObject("Pick a surface", 8)
If (VarType(srf) <> vbString) Then Exit Sub
domU = .SurfaceDomain(srf, 0)
domInput(0) = .GetReal("U Param, input Real Number between " & CStr(DomU(0)) & " and " & CStr(DomU(1)), DomU(0), DomU(0), DomU(1))
domV = .SurfaceDomain(srf, 1)
domInput(1) = .GetReal("V Param, input Real Number between " & CStr(DomV(0)) & " and " & CStr(DomV(1)), DomV(0), DomV(0), DomV(1))
arrdata = .SurfaceCurvature(srf, domInput)
tanVec = .AddLine(arrdata(0), .PointAdd(arrdata(0), arrdata(1)))