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=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,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=green,frames=50,thickness=2):
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=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,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=green,frames=50,thickness=2):
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=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,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=green,frames=50,thickness=2):
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=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,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=green,frames=50,thickness=2):
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-cos(n*t);
y:=y0-sin(n*t);
p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,frames=50):
q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,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=green,frames=50,thickness=2):
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=gold,frames=50,thickness=2):
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-cos(n*t);
y:=y0-sin(n*t);
p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,frames=50):
q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,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=green,frames=50,thickness=2):
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=gold,frames=50,thickness=2):
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-cos(n*t);
y:=y0-sin(n*t);
p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,frames=50):
q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,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=green,frames=50,thickness=2):
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=gold,frames=50,thickness=2):
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-cos(n*t);
y:=y0-sin(n*t);
p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=red):
p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=blue):
p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=blue,frames=50):
q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,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=green,frames=50,thickness=2):
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=gold,frames=50,thickness=2):
display(p1,p2,p3,p4,q3,q4);