FPG 5: Poncelet, Trilinear Polars, Harmonic Nets

In this lecture we discuss the fascinating notion of trilinear polarity, which was developed by the french mathematician Poncelet to interrelate points and lines. Using previously discussed results such as Desargue’s Theorem, we prove that Poncelet’s construction method does indeed yield a straight line s, which is the trilinear polar of a point S with respect to a triangle. We also discuss the idea of harmonic nets. When working upon a continuum these curious objects are infinite sets of collinear points,