On the Theorem of the Three Perpendiculars

TL;DR

This paper extends the classical theorem of the three perpendiculars to n-dimensional space forms, demonstrating its validity beyond Euclidean space.

Contribution

The paper generalizes the theorem of the three perpendiculars to arbitrary n-dimensional space forms, broadening its geometric applicability.

Findings

The theorem holds in all n-dimensional space forms.

The proof is valid for both Euclidean and non-Euclidean geometries.

Extension of classical geometry results to higher dimensions.

Abstract

We show that the theorem of the three perpendiculars holds in any n-dimensional space form.