Mathematical Experiment 4

Construct a sphere.

Construct a wedge as thus:

Construct this pattern on the sphere.

Design this "beach ball."

Construct this pattern on the ball. One part is given by


l = 1
c = r + s
p = r
0 r
p, 0 s p

Construct this pattern on the ball. One part is given by


l = 1
c = r
p = r + s
0 r p, 0 s p

Construct the space curve given in spherical coordinates by


l = 1
c = t
p = 2t

There is a curve on the sphere that has a projection that looks like the curve on the right. Construct this space curve.

Construct the surface given in spherical coordinates by


 l = r
c = t
p = 2t


with (r, t) ranges over [0,1] x [0, 2p]

Divide the sphere into four congruent pieces.

Divide the sphere into six congruent pieces.

Construct the surface given by the equation :


l = sin p sin 2p


in spherical coordinates.