Fig. 2.

An explication of convenient coordinates for triangles, stemming originally from a correlation analysis. Sides are denoted by $a,b$, and c, and are opposite the corresponding vertices, $\overrightarrow{A},\overrightarrow{B}$, and $\overrightarrow{C}$. The shortest and longest sides are termed b and c respectively. The median $\overrightarrow{O}$ of the triangle is constructed as well as the vector from $\overrightarrow{B}$ to $\overrightarrow{O}$, which we term “the drop”, $\overrightarrow{X}$. The three coordinates describing the triangle are given by the lengths, X, b and by the angle between $\overrightarrow{A}-\overrightarrow{C}$ and $\overrightarrow{X}$. This angle is always less than or equal to $\pi /2$ in magnitude. Mirroring the triangle can be represented by changing the sign of this last angle.