  A theorem which is named after the American Mathematician Moris Marden states
a very surprising and interesting fact concerning the relationship between the
points of a triangle in the complex plane and the zeros of two complex
polynomials related to this triangle: "Suppose the zeroes z1, z2, and z3 of a
third-degree polynomial p(z) are non-collinear. There is a unique ellipse
inscribed in the triangle with vertices z1, z2, z3 and tangent to the sides at
their midpoints: the Steiner in-ellipse. The foci of that ellipse are the
zeroes of the derivative p'(z)." (Wikipedia contributors, "Marden's theorem",
http://en.wikipedia.org/wiki/Marden%27s_theorem). This document describes how
Scilab, a popular and powerful open source alternative to MATLAB, can be used
to visualize the above stated theorem for arbitrary complex numbers z1, z2, and
z3 which are not collinear. It is further demonstrated how the equations of the
Steiner ellipses of a triangle in the complex plane can be calculated and
plotted by applying this theorem.
