Orthocenters of triangles in the n-dimensional space

TL;DR

This paper extends the concept of orthocenters from classical 2D triangles to triangles in n-dimensional space, exploring their properties and analogies with the Euclidean case.

Contribution

It introduces a novel definition of orthocenters for triangles in R^n and analyzes their properties and similarities to the 2D orthocenter.

Findings

Defined a set of orthocenters in R^n

Established analogies with classical orthocenter properties

Explored geometric properties in higher dimensions

Abstract

In this paper we present a way to define a set of orthocenters for a triangle in the n-dimensional space R^{n} and we will see some analogies of these orthocenters with the classic orthocenter of a triangle in the Euclidean plane.