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 one-half of a torus as thus:
 Construct one-half of a torus as thus:
 Construct one-half of a torus as thus:¡@
 Design a pattern on the torus appearing as thus:
 Construct one-half of a torus consisting of two intersecting circles: These circles are known as the Villarceaux circles. > a:=2;b:=5;c:=sqrt(b^2-a^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 one-half of a torus consisting of two linking circles by rotating the circle [b cos(t), a + c sin(t), a cos(t)] (a2 + b2 = c2) about the z-axis by p.
 Construct this twisted prismatic ring to be found on the stairs between two floors of the Math Library: