Mathematical Experiment 4

 
Construct the sphere with the command "plot3d". 
r = sin s
x = r cos t
y = r sin t
z = cos s
0 < s < p, 0 < t < 2p
Construct the sphere with this pattern:
   
Construct the sphere with this pattern:
   
Construct the sphere with this pattern:
   
Construct a slice of the melon.
Construct the part of the cylinder
(x - 0.5)2 + y2 = 0.25 
lying inside the sphere
x2 + y2 + z2 =1. 
 
Construct the intersection of the cylinder
(x - 0.5)2 + y2 = 0.25  
and the sphere
x2 + y2 + z2 =1.  
Construct four mutually tangent spheres of the same size:
Construct six spheres of the same size each touching four others. 
Construct eight spheres of the same size each touching three others. 
Construct 12 spheres of the same size each touching five others.
The coordinates of vertices of a dodecahedron are:
The distance between two adjacent vertices is
Construct 20 spheres of the same size each touching three others. 
 
The coordinates of vertices of a dodecahedron are:
The distance between two adjacent vertices is