Mathematical Experiment 11

 Construct a family of 20 concentric circles:plot([[n*cos(t),n*sin(t),t=0..2*Pi]\$n=1..20], color=red,axes=none);
 Construct a family of circles each centered at [cos t, sin t] passing through the point [1,0]: x:=cos(t)+d*cos(s);y:=sin(t)+d*sin(s); t:=k*2*Pi/100; with(linalg): d:=norm([cos(t),sin(t)]-[1,0],2); plot([[x,y,s=0..2*Pi]\$k=1..100],color=red, scaling=constrained,axes=none);
 Construct a family of circles each centered at [cos t, sin t] and tangent to the x-axis: x:=cos(t)+d*cos(s);y:=sin(t)+d*sin(s); t:=k*2*Pi/100; with(linalg): d:=sin(t); plot([[x,y,s=0..2*Pi]\$k=1..100],color=red, scaling=constrained,axes=none);
 Construct a family of circles each centered at [3cos t, 3sin t] and passing through [2cos t + cos 2t, 2sin t - sin 2t]:x:=3*cos(t)+d*cos(s);y:=3*sin(t)+d*sin(s); t:=k*2*Pi/100; with(linalg): d:=norm([2*cos(t)+cos(-2*t),2*sin(t)+sin(-2*t)]-[3*cos(t),3*sin(t)],2); plot([[x,y,s=0..2*Pi]\$k=1..100],color=red, scaling=constrained,axes=none);
 Construct a family of circles each centered at [4cos t, 4sin t] and passing through [3cos t + cos 3t, 3sin t - sin 3t]:x:=4*cos(t)+d*cos(s);y:=4*sin(t)+d*sin(s); t:=k*2*Pi/100; with(linalg): d:=norm([3*cos(t)+cos(-3*t),3*sin(t)+sin(-3*t)]-[4*cos(t),4*sin(t)],2); plot([[x,y,s=0..2*Pi]\$k=1..100], color=red,scaling=constrained,axes=none);
 Construct a family of ellipses enveloping the astroid:plot([[(1-k/25)*cos(t),k/25*sin(t),t=0..2*Pi]\$k=0..25], color=red,scaling=constrained,axes=none);
 Construct the line segments joining (cos(t),0) with (0,sin(t)) as t ranges over [0,2p]. > x:=cos(t); > y:=sin(t); > m:=[[x,0],[0,y]]; > t:=n*Pi/50; > plot([m\$n=1..100],color=green, scaling=constrained,axes=none); ¡@
 Construct the velocity vector field along a constant motion around a circle.
 Construct the line segments joining  [cos(t),sin(t)] with [cos(2t),sin(2t)]  as t ranges over [0,2p].
 Construct the line segments joining [cos(t),sin(t)] with [cos(3t),sin(3t)] as t ranges over [0,2p].
 Construct this pattern: