2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64273A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the triangle sequence. We give a new criterion for when a triangle sequence uniquely describes a pair of numbers and give the first explicit examples of triangle sequences that do not uniquely describe a pair of reals. Finally, this dual approach yields that the triangle sequence is topologically strongly mixing, meaning in particular that it is topologically ergodic.58 pages, 15 figuresNumber Theory11J70, 11K50, 11A55text