Pappus' Theorem is a major result in projective geometry. I have discovered a construction involving several interlocking applications of Pappus' theorem that has several very nice properties that make it an interesting construction to study. I am nearly finished writing up the results in a paper entitled "From Pappus' Theorem to the Twisted Cubic." This paper explains this construction then investigates it heavily. I found that this construction is best understood by thinking about it as a dynamical system in projective three space that is related to the geometry of the twisted cubic. My main result is the identification of a double branched covering map of projective three space that is rational and acts trivially on the space of secants to the twisted cubic.
This web page is meant to describe this construction in a not so rigorous fashion and includes many Java Applets that aid in visualization and understanding of the construction. The construction is organized into a sequence of steps that lead the viewer through the construction which is a sequence of important observations interdispersed inside several pages of background material. Here is a list of the pages (its best to start at the introduction).