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May 2018 Generating Stern-Brocot Type Rational Numbers with Mediants
Harold Reiter, Arthur Holshouser
Missouri J. Math. Sci. 30(1): 93-104 (May 2018). DOI: 10.35834/mjms/1534384959

Abstract

The Stern–Brocot tree is a method of generating or organizing all fractions in the interval \((0,1)\) by starting with the endpoints \(\frac{0}{1} \) and \(\frac{1}{1}\) and repeatedly applying the mediant operation: \(m\left( \frac{a}{b},\frac{c}{d} \right) =\frac{a+c}{b+d}\). A recent paper of Aiylam considers two generalizations: one is to apply the mediant operation starting with an arbitrary interval \(\left( \frac{a}{b},\frac{c}{d} \right)\) (the fractions must be non-negative), and the other is to allow arbitrary reduction of generated fractions to lower terms. In the present paper, we give simpler proofs of some of Aiylam's results, and we give a simpler method of generating just the portion of the tree that leads to a given fraction.

Citation

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Harold Reiter. Arthur Holshouser. "Generating Stern-Brocot Type Rational Numbers with Mediants." Missouri J. Math. Sci. 30 (1) 93 - 104, May 2018. https://doi.org/10.35834/mjms/1534384959

Information

Published: May 2018
First available in Project Euclid: 16 August 2018

zbMATH: 06949054
MathSciNet: MR3844395
Digital Object Identifier: 10.35834/mjms/1534384959

Subjects:
Primary: 11B57

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 1 • May 2018
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