A measure for the chirality of triangles

TL;DR

This paper introduces a quantitative measure for triangle chirality, distinguishing between symmetric and asymmetric triangles, with potential applications in geometric analysis and symmetry detection.

Contribution

The paper proposes a novel measure, $X ext{delta}$, to quantify the chirality of triangles, differentiating symmetric from asymmetric configurations.

Findings

$X ext{delta}$ is zero for equilateral and isosceles triangles.

$X ext{delta}$ is positive for left-handed scalene triangles.

$X ext{delta}$ is negative for right-handed scalene triangles.

Abstract

A measure for the description of the chirality of triangles is introduced. The measure $X\delta$ is zero for triangles with at least one mirror axe, i.e. equilateral or isosceles triangles, and positive or negative for scalane, i.e. left or right handed triangles, respectively.