Parabola And Its Normals

The parabola is defined by these equations:
c(t) = [ 1/param* t^2 , t ]
The caustic of its normals is the cubic y^2 = x^3.

If t1+t2+t3 = 0, then the normals at c(t1), c(t2), c(t3)
all three intersect in one point. Since the parabola
normals are tangents to the caustic, this property of
the caustic tangents is called a "geometric addition".