Just uploaded, in message 1, the corrected _Balloon2 script, which is using the simple formula, without cn or dn.

Added a modulus k slider to create other, non-mylar shapes, which are likely not physics based.
For a modulus k = -0.908908557548541+, the origin is (very nearly) crossed, and a revolve results in a solid.

The value was found by using a wide slider with very narrow range -0.9089056 to -0.9089055, then sliding until the z axis is crossed just above or below
the origin. More decimals can be manually added.

For the mylar balloon curve, the aspect ration (Thickness/Diameter) = 0.599+ approximately, is now correct.
Also, geodesics could be calculated for the mylar balloon curve.

- Brian