An application of Pappus' Involution Theorem in euclidean and non-euclidean geometry

TL;DR

This paper demonstrates how Pappus' Involution Theorem can be applied to prove theorems in both Euclidean and non-Euclidean geometries, including polygons and higher-dimensional cases.

Contribution

It introduces new applications of Pappus' Involution Theorem to Euclidean and non-Euclidean polygons and extends these results to n-dimensional Euclidean geometry.

Findings

Proved theorems about non-Euclidean triangles using Pappus' Involution Theorem

Extended theorems to Euclidean and non-Euclidean polygons of various types

Formulated an n-dimensional Euclidean version of the theorems

Abstract

Pappus' Involution Theorem is a powerful tool for proving theorems about non-euclidean triangles and generalized triangles in Cayley-Klein models. Its power is illustrated by proving with it some theorems about euclidean and non-euclidean polygons of different types. A $n$-dimensional euclidean version of these theorems is stated too.