Illumination of Pascal's Hexagrammum and Octagrammum Mysticum

Abstract

We prove general results which include classical facts about 60 Pascal's lines as special cases. Along similar lines we establish analogous results about configurations of 2520 conics arising from Mystic Octagon. We offer a more combinatorial outlook on these results and their dual statements. Bezout's theorem is the main tool, however its application is guided by the empirical evidence and computer experiments with program Cinderella. We also emphasize a connection with $k$-nets of algebraic curves.