0
$\begingroup$

The middle “hyperboloid” part of the solid of revolution is determined entirely by a single edge of the cube that does not touch one of the axis vertices - there are six such edges. Mark these on your cube. Consider one of these edges. More importantly, consider its edge segment between $(1,0,1)$ and $(0,0,1)$ as well as a separate axis segment between the two points on the planes that the axis of rotation passes through - the edge and axis segments are skew segments (i.e. not parallel, but don’t cross either . . . a phenomenon allowed by 3-d space).

I'm wondering how to:

• Parameterize the edge and axis segments – i.e. find vector-valued functions with appropriate domain restrictions to represent these segments.

•Make a change of parameter so that the domain of each of your vector-valued functions is the same. Moreover, this domain must be the same length as the length of the axis segment.

2 Answers 2