On Faster Convergence of the Bisection Method for all Triangles

Let <!-- MATH $\Delta ABC$ --> be a triangle with vertices A, B, and C. It is "bisected" as follows: choose a/the longest side (say AB) of <!-- MATH $\Delta ABC$ --> , let D be the midpoint of AB, then replace <!-- MATH $\Delta ABC$ --> by two triangles <!-- MATH $\Delta ADC$ --> and <!-- MATH $\Delta DBC$ --> .