2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223203A new classification scheme for real numbers is given, motivated by ideas from statistical mechanics in general and work of Knauf and of Fiala and Kleban in particular. Critical for this classification of a real number will be the Diophantine properties of its continued fraction expansion.Number TheoryMathematical Physics11J82 (Primary), 11B57, 11J70, 82B05, 82B26 (Secondary)text