12

§@·~12

1.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.
2.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.
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.
5.Construct 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 z=4-(xy)^(1/2) (x2 + y2 + z2)2 = 2z(x2+ y2)
11.Construct the same surface located above the disc x^2+y^2<=4
12.Construct the graph of the function xy/(x^2+y^2) as (x,y) ranges over the unit disc.
13.Construct the solid enclosed by the paraboloids z = 5x2 + 5y2 and z = 6 - 7x2 -y2.