Ford circles, continued fractions, and best approximation of the second kind
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🧮 math.NT
math.MG
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alphabestcirclescontinuedfordkindsecondapproximation
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We give an elementary geometric proof using Ford circles that the convergents of the continued fraction expansion of a real number $\alpha$ coincide with the rationals that are best approximations of the second kind of $\alpha$.
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