> restart;
> with(plots):
> n:=2;
> x0:=n*cos(t);y0:=n*sin(t);
> x:=x0-cos(n*t);y:=y0-sin(n*t);
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,

   color=cyan,frames=50,thickness=5):
> display(p1,p2,p3,p4);

> restart;
> with(plots):
> n:=3;
> x0:=n*cos(t);y0:=n*sin(t);
> x:=x0-cos(n*t);y:=y0-sin(n*t);
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,

   color=cyan,frames=50,thickness=5):
> display(p1,p2,p3,p4);

> restart;
> n:=-2;
> with(plots):
> x0:=n*cos(t);y0:=n*sin(t);
> x:=x0-cos(n*t);y:=y0-sin(n*t);
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50,thickness=3):
> display(p1,p2,p3,p4);

> restart;
> n:=-3;
> with(plots):
> x0:=n*cos(t);y0:=n*sin(t);
> x:=x0-cos(n*t);y:=y0-sin(n*t);
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50,thickness=3):
> display(p1,p2,p3,p4);

> restart;
> n:=-2;
> with(plots):
> x0:=n*cos(t);y0:=n*sin(t);
> x1:=-cos(n*t);y1:=-sin(n*t);
> x:=x0+x1;y:=y0+y1;
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50,thickness=3):
> q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50):
> xxx:=expand((1-s)*x1+s*x);yyy:=expand((1-s)*y1+s*y);
> q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,

  scaling=constrained,axes=none,color=green,frames=6,thickness=50):
> display(p1,p2,p3,p4,q3,q4);

> restart;
> n:=-3;
> with(plots):
> x0:=n*cos(t);y0:=n*sin(t);
> x1:=-cos(n*t);y1:=-sin(n*t);
> x:=x0+x1;y:=y0+y1;
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50,thickness=3):
> q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50):
> xxx:=expand((1-s)*x1+s*x);yyy:=expand((1-s)*y1+s*y);
> q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50,thickness=3):
> display(p1,p2,p3,p4,q3,q4);
　

> restart;
> n:=3;
> with(plots):
> x0:=n*cos(t);y0:=n*sin(t);
> x1:=-cos(n*t);y1:=-sin(n*t);
> x:=x0+x1;y:=y0+y1;
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50,thickness=3):
> q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50):
> xxx:=expand((1-s)*x1+s*x);yyy:=expand((1-s)*y1+s*y);
> q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50,thickness=3):
> display(p1,p2,p3,p4,q3,q4);

> restart;
> n:=2;
> with(plots):
> x0:=n*cos(t);y0:=n*sin(t);
> x1:=-cos(n*t);y1:=-sin(n*t);
> x:=x0+x1;y:=y0+y1;
> p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):
> p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],

   scaling=constrained,axes=none,color=yellow):
> p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50):
> xx:=expand((1-s)*x0+s*x);
> yy:=expand((1-s)*y0+s*y);
> p4:=animate([xx,yy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=cyan,frames=50,thickness=3):
> q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50):
> xxx:=expand((1-s)*x1+s*x);yyy:=expand((1-s)*y1+s*y);
> q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,

   scaling=constrained,axes=none,color=green,frames=50,thickness=3):
> display(p1,p2,p3,p4,q3,q4);