Farey Tree

tree level

12

The Farey tree contains all the irreducible rational numbers between 0 and 1. It is constructed in stages consisting of the rationals

a/n

with

1<=a<=n

and

gcd(a,n)=1

. Each "child" is obtained by using Farey addition. A vertex labeled with

e/f

is the child of the vertices

a/b

and

c/d

if

e/f=(a+c)/(b+d)

.

This Demonstration is based on[1, Chapter 1].

[1] A. Hatcher, Topology of Numbers, New York: Cornell University, 2018.

Carlos Enrique Nosa Guzman