EX12
1.Construct
a surface .
2.Construct
a solid
3.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)
4.Construct
the hyperboloid of two sheets given by the equation
x2 - y2
- z2 = 1.
5Construct
the smallest sphere that contains the six circles each of which is inscribed
in a face of a cube.
6.Construct
the part of the sphere x2 + y2 + z2 =1
lying
outside the cylinder (x - 0.5)2 + y2 = 0.25.
7.Construct
three tori of the same size each enclosing the other two.
8.Show
that a certain section of a cube consists of a hexagon.
9.Construct
the surface given by the equation
(x2 +
y2 + z2)2 = 2z(x2+ y2)
10.Construct
the surface given by the equation
over
the square [-2, 2] x [-2,2].
11.Construct
the same surface located above the disc
12.Construct
the graph of the function as (x,y) ranges over the unit disc.
13.Construct
the solid enclosed by the paraboloids z = 5x2 + 5y2 and z = 6 - 7x2 -y2.