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Mathematical Experiment 15

Construct
these Borromean rings.

Construct the "corkscrew" given by [cos(u)cos(v),sin(u)sin(v),sin(v)+u].

Construct
the graph of the function f(u,v) = u^{2}v^{4} as (u,v)
ranges over the unit disk.

Construct Scherk's Fifth Surface given by
[arcsinh(u),arcsinh(v),arcsin(uv)]

Construct the pseudosphere given by
[cos(u)*sin(v),sin(u)*sin(v),cos(v)+log(tan(v/2))]

Construct the crosscap given by
[cos u sin(2v), sin u sin(2v), cos^{2}v - cos^{2}u
sin^{2}v]

Construct the Ennerper's Surface given by
[u - u^{3}/3 + uv^{2}, v - v^{3}/3 + vu^{2},
u^{2 }- v^{2}]

When a cube is rotating about its main diagonal, describe the
region wiped out by the cube.