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arXiv · 0912.1997

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

Ian Short
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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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Ian Short. 2009-12-10. Ford circles, continued fractions, and best approximation of the second kind. https://arxiv.org/abs/0912.1997

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