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

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

2009-12-10

arxiv.org/abs/0912.1997v1

Mathematics

Number Theory

8 pages, 6 figures

Scientific paper

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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