# Mathematical Experiment 12

 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 graph associated with the logistic equation x ' = ax(1-x) ¡@ with a=3.7 > x:=0.7; > a:=3.7; > y:=a*x*(1-x); > m:=[ ]; > for k to 100 do 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:
 Construct the circles with center at (cos(t),sin(t)) passing through the point (1,0) with t ranging over [0,2p].
 Construct the circles with center at (cos(t),sin(t)) and tangent to the y-axis with t ranging over [0,2p].
 Construct the circles with center at (cos(t),sin(t)) and and passing through (2cos(t)/3+cos(2t)/3,2sin(t)/3+sin(2t)/3)  with t ranging over [0,2p].
 Construct this figure:
 Construct this pattern:
 Construct the reflections of a light ray inside a square: > m:=1.7123:x:=0:y:=0:v:=[ [x,y] ]: > for k to 100 do xx:=floor(x)+1:yy:=floor(y)+1: if (yy-y)>m*(xx-x) then x:=xx:y:=m*x else y:=yy:x:=y/m: fi: v:=[op(v),[1-abs(x-2*floor(x/2)-1),1-abs(m*x-2*floor(m*x/2)-1)]] od: > plot(v,scaling=constrained); ¡@ ¡@