12

Summer Session 12 2000,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.	12-1
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.	12-2
Construct the Klein bottle with parametric equation 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)	12-3
Construct the hyperboloid of two sheets given by the equation x^2 - y^2 - z^2 = 1.	12-4
Construct the smallest sphere that contains the six circles each of which is inscribed in a face of a cube.	12-5
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.	12-6
Construct three tori of the same size each enclosing the other two.	12-7
Show that a certain section of a cube consists of a hexagon.	12-8
Construct the surface given by the equation (x2 + y2 + z2)^2 = 2z(x^2+ y^2)	12-9
Construct the surface given by the equation Z=4-sqrt(abs(x*y)) over the square [-2, 2] x [-2,2]. Construct the same surface located above the disc x^2+y^2<=4	12-10-1 12-10-2
Construct the graph of the function xy/(x^2+y^2) as (x,y) ranges over the unit disc.	12-11
Construct the solid enclosed by the paraboloids z = 5x^2 + 5y^2 and z = 6 - 7x^2 -y^2.	12-12