Mathematical Experiment 12

Construct a surface which appears as a triangle along the x-axis,
appears as a triangle along the y-axis,
apprears as an astroid along the z-axis
and whose z-cross section are formed by ellipses.

Construct a solid which appears as an equilateral triangle along the x-axis,
appears as a half-ellipse along the y-axis,
appears as a circle along the z-axis.

Construct the Klein bottle with parametric equations
x = (a+cos(u/2) sin(v) - sin(u/2) sin(2v)) cos(u)
y = (a+cos(u/2) sin(v) - sin(u/2) sin(2v)) sin(u)
z = sin(u/2) sin(v) + cos(u/2) sin(2v)

Construct the hyperboloid of two sheets given by the equation
x2 - y2 - z2 = 1.

Construct the smallest sphere that contains the six circles each of which is inscribed in a face of a cube.

Construct the part of the sphere
x2 + y2 + z2 =1
lying outside the cylinder
(x - 0.5)2 + y2 = 0.25.

Construct three tori of the same size each enclosing the other two.

Show that a certain section of a cube consists of a hexagon.

Construct the surface given by the equation
(x2 + y2 + z2)2 = 2z(x2+ y2)

Construct the surface given by the equation
over the square [-2, 2] x [-2,2].
Construct the same surface located above the disc

Construct the graph of the function
as (x,y) ranges over the unit disc.

Construct the solid enclosed by the paraboloids
z = 5x2 + 5y2 and z = 6 - 7x2 -y2.