Summer Session 12

August 10

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
x^{2} - y^{2} - z^{2} = 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
x^{2} + y^{2} + z^{2} =1
lying outside the cylinder
(x - 0.5)^{2} + y^{2} = 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
(x^{2} + y^{2} + z^{2})^{2} = 2z(x^{2}+
y^{2})

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 = 5x^{2} + 5y^{2} and z = 6 - 7x^{2}
-y^{2}.