4-12.mws

Construct this figure:

>

> restart;

> x:=cos(t);

x := cos(t)

> y:=sin(t);

y := sin(t)

> x1:=3/4*x+1/4*cos(3*t);

x1 := 3/4*cos(t)+1/4*cos(3*t)

> y1:=3/4*y-1/4*sin(3*t);

y1 := 3/4*sin(t)-1/4*sin(3*t)

> r:=((x-x1)^2+(y-y1)^2)^(1/2);

r := sqrt((1/4*cos(t)-1/4*cos(3*t))^2+(1/4*sin(t)+1...

> m:=[x+r*sin(s),y+r*cos(s),s=-Pi..Pi];

m := [cos(1/50*k*Pi)+sqrt((1/4*cos(1/50*k*Pi)-1/4*c...
m := [cos(1/50*k*Pi)+sqrt((1/4*cos(1/50*k*Pi)-1/4*c...
m := [cos(1/50*k*Pi)+sqrt((1/4*cos(1/50*k*Pi)-1/4*c...
m := [cos(1/50*k*Pi)+sqrt((1/4*cos(1/50*k*Pi)-1/4*c...
m := [cos(1/50*k*Pi)+sqrt((1/4*cos(1/50*k*Pi)-1/4*c...

> t:=k*Pi/50;

t := 1/50*k*Pi

> w:=evalf(m):

> plot([w$k=1..100],color=red,scaling=constrained,axes=none);

[Maple Plot]

>