Construct this pretty flower:

> plot((1+cos(3*t)+sin(3*t)^2),t=0..2*Pi,coords=polar,axes=none,scaling=constrained);

Construct the line segments joining (cos(t),0) with (0,sin(t)) as t ranges over [0,2p].

> m:=[[cos(t),0],[0,sin(t)]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

Construct the velocity vector field along a constant motion around a circle.

> restart:

> x:=cos(t);

> y:=sin(t);

> m:=[[x,y],[x+diff(x,t),y+diff(y,t)]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

Construct this figure: x

> restart:

> x:=cos(t);

> y:=sin(t);

> m:=[[x,y],[x+t*diff(x,t),y+t*diff(y,t)]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

Construct the line segments joining [cos(t),sin(t)] with [cos(2t),sin(2t)] as t ranges over [0,2p].

> restart:

> x1:=cos(t);

> y1:=sin(t);

> x2:=cos(2*t);

> y2:=sin(2*t);

> m:=[[x1,y1],[x2,y2]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

Construct this figure:

> restart:

> x1:=cos(t);

> y1:=sin(t);

> x2:=cos(3*t);

> y2:=sin(3*t);

> m:=[[x1,y1],[x2,y2]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=blue,scaling=constrained,axes=none);

Construct this graph associated with the logistic equation
x ' = ax(1-x)

> restart:

> x:=0.7;

> a:=3.7;

> y:=a*x*(1-x);

> m:=[];

> for k to 100do m:=[op(m),[x,x],[x,y]]:x:=y:y:=a*x*(1-x):od:

> plot(m,scaling=constrained);

Draw 20 concentric circles as thus:

> x:=t*cos(r);

> y:=t*sin(r);

> m:=[[x,y,r=0..2*Pi]$t=0..20]:

> plot(m,scaling=constrained,axes=none,color=green);

Construct the circles with center at (cos(t),sin(t)) passing through the point (1,0) with t ranging over [0,2p].

> restart:

> x1:=cos(t):

> y1:=sin(t):

> r:=sqrt(2-2*cos(t)):

> t:=n*2*Pi/100:

> plot([[x1+r*cos(s),y1+r*sin(s),s=0..2*Pi]$n=1..100],scaling=constrained,axes=none,color=green);

>