Ford circles, continued fractions, and best approximation of the second kind

2009/12/10 by Ian Short, Short, Ian
Mathematics · #11J70 #FOS: Mathematics #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0912.1997

openalex publication_date 2009/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an elementary geometric proof using Ford circles that the convergents of the continued fraction expansion of a real number α coincide with the rationals that are best approximations of the second kind of α.

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