2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163947A relationship between continued fractions and Weyl groupoids of Cartan schemes of rank two is found. This allows to decide easily if a given Cartan scheme of rank two admits a finite root system. We obtain obstructions and sharp bounds for the entries of the Cartan matrices. Key words: Cartan matrix, continued fraction, Nichols algebra, Weyl groupoid23 pagesGroup TheoryQuantum Algebra20F55, 11A55, 16W30text