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

ρ = 1
θ = r + s
φ = r
0 ≦ r ≦ p, 0 ≦ s ≦ p

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

ρ = 1
θ = r
φ = r + s
0 ≦ r ≦ p, 0 ≦ s ≦ p

Construct the space curve given in spherical coordinates by

ρ = 1
θ = t
φ = 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

ρ = r
θ = t
φ = 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 :

ρ = sin φ sin 2φ

in spherical coordinates.