The Stern – Brocot tree

Abstract

The present paper narrates an imaginary conversation between the author and her imaginary
uncle Pedro. The subject of this conversation is the construction of a binary tree from mediant
fractions, baptized with the last names of the german mathematician Moritz Stern and
the french clockmaker and amateur mathematician Achille Brocot. In his exposition on the
Stern-Brocot tree, uncle Pedro explains what the mediant fraction is and exposes some historical
data about how the mathematician Nicolás Chuquet used it to solve equations. Finally,
he proves that in this tree each positive and irreducible fraction appears exactly once.