L6.html

> with(plots);
spacecurve([t*cos(t),t*sin(t),t],t=0..100,numpoints=1000,axes=normal);

> spacecurve([t,t^2,t^3],t=-3..3,numpoints=1000,color=black,axes=normal);

> spacecurve([(cos(3*t)+2)*cos(2*t),(cos(3*t)+2)*sin(2*t),sin(2*t)],t=0..2*Pi,numpoints=1000,axes=normal,color=black);

> with(plots);
> F:=spacecurve([(cos(3*t)+2)*cos(2*t),(cos(3*t)+2)*sin(2*t),sin(3*t)],t=0..2*Pi,numpoints=1000,color=red,thickness=4);
G:=plot3d([(cos(u)+2)*cos(s),(cos(u)+2)*sin(s),sin(u)],s=0..2*Pi,u=0..2*Pi,style=patch,transparency=0.5);
display({F, G});

The same curve (thick red) and the thorus

>	with(plots);
>	*F:=spacecurve([(cos(3t)+2)cos(2t),(cos(3t)+2)sin(2t),sin(3t)],t=0..2Pi,numpoints=1000,color=red,thickness=4);* G:=plot3d([(cos(u)+2)cos(s),(cos(u)+2)sin(s),sin(u)],s=0..2Pi,u=0..2Pi,style=patch,transparency=0.5); display({F, G});