Mathematical Experiment 3

Construct a cylinder with a slit along a spiral.

Wrap the graph of y = sin 2x around a cylinder.

Place the smooth surface on top on the above surface.

Construct the Monkey's Saddle:

Carve out the Monkey's Saddle out of a solid cylinder:

Construct one-half of a solid cylinder as thus:

Construct the region enclosed by the two cylinders with equation

x2 + z2 = 1

y2 + z2 = 1

Construct one-half of the above surface as thus

Construct this surface:

Construct this one-half of a solid torus: