A formulation of Euclidean geometry leading to recognition of a new class of algebra isomorphism invariants

TL;DR

This paper introduces alternative Euclidean geometry postulates that reveal new algebraic invariants and geometries related to real finite-dimensional unital associative algebras.

Contribution

It proposes a novel formulation of Euclidean geometry that uncovers a new class of algebra isomorphism invariants and associated geometries.

Findings

New class of algebra invariants identified

Alternative Euclidean postulates lead to novel geometries

Connections established between geometry and algebra invariants

Abstract

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.