A note on the planar triangles in Minkowski spacetime

TL;DR

This paper explores basic properties of triangles in 2D Minkowski spacetime, demonstrating that classical Euclidean theorems like Feuerbach's also hold in this non-Euclidean setting, and discusses centers of triangles.

Contribution

It provides an elementary analysis of triangle geometry in Minkowski spacetime, highlighting the validity of Euclidean theorems in this context and examining triangle centers.

Findings

Feuerbach's theorem holds in Minkowski plane

Properties of incenter and excenters are discussed

Basic triangle geometry extends to Minkowski spacetime

Abstract

The geometry of 2D Minkowski spacetime $\mathbb{R}^{1,1}$ (or Minkowski plane) is similar but fundamentally different from the more familiar Euclidean plane geometry. This note gives an elementary discussion on some basic properties of a triangle on the Minkowski plane. In particular, we show that the theorem of Feuerbach also holds and a use of the incenter/excenters is pointed out.