Representation of similar triangles in $\mathbb{R}^{3}$

TL;DR

This paper extends Dhar and Sinha's 2D graphic classification of triangles to three-dimensional space, providing a new visualization method and analyzing specific triangle classes quantitatively.

Contribution

It generalizes the 2D triangle similarity representation to 3D and includes a quantitative analysis of certain triangle classes.

Findings

Successful extension of triangle classification to $\

in $ ext{R}^3$

New graphic representation method for 3D similar triangles,

Abstract

In 1994, Dhar and Sinha provided a graphic representation in $\mathbb{R}^{2}$ of the classification of triangles based on similarity. In this article, we briefly recall their treatment and offer a generalization by providing a graphic representation in $\mathbb{R}^{3}$. Towards the end of this article, we make an attempt to offer a quantitative analysis of some particular class of triangles.