1 Construct the sphere with the command "plot3d".

> r:=sin(s):

> x:=r*cos(t):

> y:=r*sin(t):

> z:=cos(s):

> plot3d([x,y,z],s=0..Pi,t=0..2*Pi,scaling=constrained,axes=none);

2 Construct the sphere with this pattern:

> r:=sin(s):

> x:=r*cos(t):

> y:=r*sin(t):

> z:=cos(s):

> a:=plot3d([x,y,z],s=0..Pi,t=0..Pi/2,scaling=constrained,color=pink):

> b:=plot3d([x,y,z],s=0..Pi,t=Pi/2..Pi,scaling=constrained,color=green):

> c:=plot3d([x,y,z],s=0..Pi,t=Pi..3*Pi/2,scaling=constrained,color=blue):

> d:=plot3d([x,y,z],s=0..Pi,t=3*Pi/2..2*Pi,scaling=constrained,color=yellow):

> with(plots):

Warning, the name changecoords has been redefined

3 Construct the sphere with this pattern:

> restart:

> r:=sin(s):

> x:=r*cos(t):

> y:=r*sin(t):

> z:=cos(s):

> a:=plot3d([x,y,z],s=0..Pi,t=0..Pi/3,scaling=constrained,color=pink):

> b:=plot3d([x,y,z],s=0..Pi,t=Pi/3..2*Pi/3,scaling=constrained,color=green):

> c:=plot3d([x,y,z],s=0..Pi,t=2*Pi/3..Pi,scaling=constrained,color=blue):

> d:=plot3d([x,y,z],s=0..Pi,t=Pi..4*Pi/3,scaling=constrained,color=yellow):

> e:=plot3d([x,y,z],s=0..Pi,t=4*Pi/3..5*Pi/3,scaling=constrained,color=red):

> f:=plot3d([x,y,z],s=0..Pi,t=5*Pi/3..2*Pi,scaling=constrained,color=brown):

> with(plots):

> display(a,b,c,d,e,f);

4 Construct the sphere with this pattern:

> restart:

> r:=sin(s):

> x:=r*cos(t+s):

> y:=r*sin(t+s):

> z:=cos(s):

> a:=plot3d([x,y,z],s=0..Pi,t=0..Pi/3,scaling=constrained,color=pink):

> b:=plot3d([x,y,z],s=0..Pi,t=Pi/3..2*Pi/3,scaling=constrained,color=green):

> c:=plot3d([x,y,z],s=0..Pi,t=2*Pi/3..Pi,scaling=constrained,color=blue):

> d:=plot3d([x,y,z],s=0..Pi,t=Pi..4*Pi/3,scaling=constrained,color=yellow):

> e:=plot3d([x,y,z],s=0..Pi,t=4*Pi/3..5*Pi/3,scaling=constrained,color=red):

> f:=plot3d([x,y,z],s=0..Pi,t=5*Pi/3..2*Pi,scaling=constrained,color=brown):

> with(plots):

Warning, the name changecoords has been redefined

5 Construct the part of the cylinder (x - 0.5)^2 + y^2 = 0.25 lying inside the sphere x^2 + y^2 + z^2 =1

> restart:

> x:=0.5+0.5*cos(t):

> y:=0.5*sin(t):

> z1:=sqrt(1-x^2-y^2):

> z2:=-z1:

> z:=(1-s)*z1+s*z2:

> plot3d([x,y,z],s=0..1,t=0..2*Pi,grid=[5,80],scaling=constrained);

6 Construct the intersection of the cylinder (x - 0.5)^2 + y^2 = 0.25 and the sphere x^2 + y^2 + z^2 =1.

> restart:

> x:=0.5+0.5*cos(t):

> y:=0.5*sin(t):

> z1:=sqrt(1-x^2-y^2):

> z2:=-z1:

> z:=(1-s)*z1+s*z2:

> a:=plot3d([x,y,z],s=0..1,t=0..2*Pi,grid=[5,100],scaling=constrained,color=red):

>

> x:=0.5+r*cos(t):

> y:=r*sin(t):

> z:=sqrt(1-x^2-y^2):

> b:=plot3d([x,y,z],r=0..0.5,t=0..2*Pi,grid=[5,100],scaling=constrained,color=blue):

> c:=plot3d([x,y,-z],r=0..0.5,t=0..2*Pi,grid=[5,100],scaling=constrained,color=yellow):

> with(plots):

Warning, the name changecoords has been redefined

7 Construct the sphere with the command "sphere" in "plottools".

> restart:

> with(plottools):

> a:=sphere([0,0,0],1):

> with(plots):

Warning, the name changecoords has been redefined

8 Construct eight spheres of the same size each touching three others.

> restart:

> with(plottools):

> a1:=sphere([1,1,1],1,grid=[35,35],color=yellow):

> a2:=sphere([1,1,-1],1,grid=[35,35],color=brown):

> a3:=sphere([1,-1,1],1,grid=[35,35],color=pink):

> a4:=sphere([1,-1,-1],1,grid=[35,35],color=blue):

> a5:=sphere([-1,1,1],1,grid=[35,35],color=red):

> a6:=sphere([-1,1,-1],1,grid=[35,35],color=green):

> a7:=sphere([-1,-1,1],1,grid=[35,35],color=cyan):

> a8:=sphere([-1,-1,-1],1,grid=[35,35],color=gold):

> with(plots):

Warning, the name changecoords has been redefined

9 Construct four mutually tangent spheres of the same size:

> restart:

> with(plottools):

> a1:=sphere([1,1,1],2^(1/2),grid=[35,35],color=yellow):

> a2:=sphere([-1,-1,1],2^(1/2),1,grid=[35,35],color=pink):

> a3:=sphere([1,-1,-1],2^(1/2),1,grid=[35,35],color=blue):

> a4:=sphere([-1,1,-1],2^(1/2),1,grid=[35,35],color=red):

> with(plots):

Warning, the name changecoords has been redefined

>