Ford circles, continued fractions, and rational approximation

Short, Ian (2011). Ford circles, continued fractions, and rational approximation. American Mathematical Monthly, 118(2) pp. 130–135.

DOI: https://doi.org/10.4169/amer.math.monthly.118.02.130

Abstract

We give an elementary geometric proof using Ford circles of a well-known theorem of Lagrange, which says that the convergents of the continued fraction expansion of a real number α coincide with the rationals that are best approximations of α.

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