Summer Session 5

July 18

Construct the envelope of the light rays emitted from a radiant point source
at infinity after reflection by the semi-circle.

Construct the envelope of the light rays emitted from a radiant point source
at the circumference after reflection by the same circle.
Construct the envelope formed by a fix diameter of a circle rolling
along a straight line.

Construct the envelope formed by a fix diameter of a circle rolling along
a fixed circle of the same size.

Construct the envelope formed by a fix diameter of a circle rolling along
a fixed circle twice the diameter.

Construct this figure:

Construct this figure:

Construct this design:

Construct the nested squares as thus:

Constructed nested triangles as thus:

Construct this pattern:

Construct the family of ellipses
as t ranges in [0,1].

Construct the concentric and coaxial ellipses of constant area:

Construct this pattern.

Construct this pattern.

Construct the reflections of a light ray trapped inside a reflective ellipse.
There are two cases.

restart;with(linalg):

> a:=5:b:=3:r:=1.34:s:=5.9;

> ll:=[a*cos(r),b*sin(r)]:l:=[a*cos(s),b*sin(s)];

> m:=[l,ll];

> for k to 200 do u:=ll-l: n:=[-b*ll[1]/a,-a*ll[2]/b]:v:=u-2*dotprod(u
, n)*n/dotprod(n,n):t:=-2*(b^2*v[1]*ll[1]+a^2*ll[2]*v[2])/(b^2*v[1]^2 +a^2*v[2]^2):lll:=ll+t*v:m:=[op(m),lll]:l:=ll:ll:=lll:od:

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