Dan Kalman ascribes to Marden, and describes it as the most amazing theorem: If three noncollinear points in the complex plane forming the vertices of a triangle are interpolated by a (monic) cubic polynomial p(z), the zeros of p'(z) are the foci of a unique ellipse (the Steiner in-ellipse) that is tangent to the sides of the triangle at the midpoints of the sides. The charm of this easy-to-state theorem that joins algebra, geometry, and complex analysis is explored with the tools of Maple.?
Maple Tips & Techniques
Dr. Robert Lopez
