Hatcher-Topology-of-Numbers · Problem 1.1.2

Continued Fractions

Mathematics — Algebraic Topology · farey-diagram-vertex-neighbors

Problem

Consider a vertex of the Farey diagram labeled

a/b

with

b > 1

. Show that of all the labels on vertices connected to the

a/b

vertex by an edge of the diagram, exactly two have denominator smaller than

b