Abstract

  In The Republic, Plato presents the analogy of the divided line in order to unify his ontological, epistemological and cosmological doctrine. It is rarely noted, however, that the divided line has mathematical applications. In this paper, we explore the relationship ofthe divided line to the problem ofderiving Pythagorean triples, that is, sets of three integers that serve as the sides of Pythagorean triangles. We also note the significance of this application within a broader context