Example triangle with our used notations. The sidelengths are denoted by x₁ = X₃ − X₂ and cyclic permutations. The interior angles of the triangle are denoted by ϕ_i, whereas φ_i are the angles that the sidelengths take with respect to the x-axis. We also show two possible definitions of its centre: The orthocenter O is at the intersection of the three altitudes (blue dashed); the centroid C is at the intersection of its three medians (red dashed). Figure adapted from Schneider et al. (2005).