Formulas generalizing Pappus and Desargues

TL;DR

This paper introduces two formulas that generalize the classical Pappus and Desargues theorems within three-dimensional vector spaces over a field, expanding their applicability beyond traditional geometric contexts.

Contribution

The paper presents novel formulas that extend Pappus and Desargues theorems to three-dimensional vector spaces over arbitrary fields.

Findings

Formulas hold in three-dimensional vector spaces over any field

Generalization of classical theorems beyond Euclidean geometry

Potential applications in algebraic geometry and vector space analysis

Abstract

The Theorems of Pappus and Desargues are generalized by two special formulas that hold in the three-dimensional vector space over a field.