Desargues theorem, its configurations, and the solution to a long-standing enumeration problem

TL;DR

This paper solves a long-standing enumeration problem for Desargues configurations, extends the results to blockline structures, and provides a transparent proof of Desargues theorem in plane and space.

Contribution

It introduces a novel enumeration of non-degenerate Desargues configurations and extends the analysis to complex blockline structures, along with a new proof of Desargues theorem.

Findings

Enumerated non-degenerate Desargues configurations

Extended results to Desargues blockline structures

Provided a transparent proof of Desargues theorem in plane and space

Abstract

We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline structures in Section 8. A transparent proof of Desargues theorem in the plane and in space is presented as a by-product of our methods.