Djordje Baralić: Pascal’s Hexagrammum and Octagrammum Mysticum

We prove several generalizations of ramarkable Pascal's theorem which
states that if we draw a hexagon inscribed in a conic section then the
three pairs of opposite sides of the hexagon intersect at three points
which lie on a straight line - the Pascal line of the hexagon. The
complete figure formed by 60 Pascal's line has amazing properties ant it
is known as Hexagrammum Mysticum. The similar results about an octagon inscribed in a conic section are known as Octagrammum Mysticum. We present an elementary combinatorial proof of those classical using Bézout's theorem as the main tool whose application is guided by the empirical evidence and computer experiments with the program Cinderella.