Mathematical Experiment 3


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


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

circle.mws

Construct this figure:

sp2.mws

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


Construct this figure:

line-nephroid.mws

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

logistic.mws
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:

concentric.mws

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

cardioid.mws

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].

epi-hypo.mws

Construct this figure:

epi-hypo-4.mws

Construct this pattern:

spiral.mws

Construct the reflections of a light ray inside a square:

reflections.mws
> 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);