When we want to use algebraic methods to discuss metrical properties of the triangle such as Feuerbach’s theorem, Simson’s line, etc., we have the dilemma that Cartesian coordinates confuse the symmetry of the triangle, whereas in areals or other triangular coordinates the metrical formulae are not sufficiently simple. A convenient alternative is to use the method of the Argand diagram: that is, to use complex coordinates (or “affixes”) x ± iy.