The Golden Section's heptagonal connections

Abstract

It is well known that the Golden Section plays an important role in the geometry of several polygons and polyhedra; the best known example is the length of a diagonal in the regular pentagon with unit side. In this contribution we show how the Golden Section appears as the solution of an enumerative problem connected with heptagons, more precisely, with heptagonal tilings of the hyperbolic plane. The results are then generalized by investigating whether it also appears in other types of hyperbolic tilings.