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);