Mathematical Experiment 2
Construct a torus.  > a:=2;c:=5;r:=c+a*cos(t); > x:=r*cos(s); > y:=r*sin(s); > z:=a*sin(t); > plot3d([x,y,z], s=0..2*Pi,t=0..2*Pi, scaling=constrained); 
Construct onehalf of a torus as thus: 
Construct onehalf of a torus as thus: 
Construct onehalf of a torus as thus: ¡@ 
Design a pattern on the torus appearing as thus: 
Construct onehalf of a torus consisting of two intersecting circles: These circles are known as the Villarceaux circles.  
> a:=2;b:=5;c:=sqrt(b^2a^2); > r:=b+a*cos(t); > x:=r*cos(s); > y:=r*sin(s); > z:=a*sin(t); > w:=solve(c*z=a*x,s); > h:=plot3d([x,y,z],s=w..w,t=0..2*Pi,scaling=constrained,lightmodel=light3,grid=[100,100]): > with(plottools): > vrml(h,"z:/usr1/data/disk3/exp02/2/4.wrl",background_color=white); 
Construct
onehalf of a
torus consisting of two linking circles by rotating the circle
[b cos(t), a + c sin(t), a cos(t)] about the zaxis by p. 

Construct this twisted prismatic ring to be found on the stairs between two floors of the Math Library: 