Reversion Porisms for Lines

Abstract

We show that the Butterfly Porism about cyclic quadrilaterals also applies to a degenerate case of a conic. Moreover, we prove that the collinearity used in this theorem is a necessary condition and we give an alternative proof for Pappus’s Hexagon Theorem. The main result is a reversion porism for polygons with an arbitrary number of vertices on two distinct lines. We define a polar line for a degenerate case of a conic and present a conjugated reversion porism. Lastly, we consider reversions on more than two lines.