For given triangles T = (A,B,C) and D = (X, Y, Z), the D-Napoleon and D-Torricelli triangles ND(T ) and TD(T ) of a triangle T = (A,B,C) are the triangles A′B′C ′ and A∗B∗C∗, where ABC ′, BCA′, CAB′, A∗BC, AB∗C, ABC∗ are similar to D. In this paper it is shown that the iteration N n D(T ) either terminates or converges (in shape) to an equilateral triangle, and that the iteration T n D (T ) eit...