Pratt sequences and n-gons Original Research Article

A Pratt sequence for an n-gon consists of n distinct lines, one through each vertex of the n-gon, which satisfy a certain cyclic product relation. If n=3, three lines through the vertices of a triangle form a Pratt sequence if and only if they are concurrent. The purpose of this paper is to generalise many familiar theorems of Euclidean geometry. We show that whenever three lines (such as the medians, angle-bisectors, altitudes, etc.) are concurrent in a triangle, then the corresponding n lines in an n-gon form a Pratt sequence.