Pratt sequences and \(n\)-gons (Q1574583)

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. Many results of this article can be summarized in the following way. Whenever three lines, one through each vertex of a triangle are concurrent (for example the medians, altitudes, angle-bisectors, etc.) then the corresponding lines in an \(n\)-gon form a Pratt sequence. Pratt sequences occur frequently throughout polygon geometry, and not just in generalizations of triangle theorems. The author illustrates this remark with a few additional examples. Some historical remarks, references and general comments are mentioned, too.