The Stern – Brocot tree
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Universidad Antonio Nariño
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The present paper narrates an imaginary conversation between the author and her imaginaryuncle Pedro. The subject of this conversation is the construction of a binary tree from mediantfractions, baptized with the last names of the german mathematician Moritz Stern andthe french clockmaker and amateur mathematician Achille Brocot. In his exposition on theStern-Brocot tree, uncle Pedro explains what the mediant fraction is and exposes some historicaldata 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.