Mathematical Experiment 2

Construct the hyperboloid of one sheet by rotating the line segment joining the point [cos t, sin t, 1] with the point [cos (a+t), sin(a+t), -1] about the z-axis, Here a is some given constant.

Decompose the hyperboloid of one sheet into two disjoint, symmetric parts with the straight line as boundary.

Construct the hyperboloid of two sheets given by the equations x = sinh u cos v
y = sinh u sin v
z = + cosh u

-2 < u < 2, 0 < v < 2p.

Construct the ellipsoid given by the equations x = 5 cos u sin v
y = 4 sin u sin v
z = 3 cos v

0 < u < 2p, 0 < v < 2p.

Construct the elliptic paraboloid given by the equations x = 2 u cos v
y = 3 u sin v
z = 3 u²

0 < u < 1, 0 < v < 2p.

Construct the intersection of the two solid cylinders

x² + y² < 1
x² + z² < 1

Construct the symmetric one-half of the surface in the previous problem,