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Abstract

Lester Ford introduced Ford circles in 1938 in order to geometrically understand the approximation of an irrational number by rational numbers. We shall construct Ford circles by a recursive geometric procedure. The Ford circles also turn out to be parameterized by the rational numbers. We introduce a new parameterization of the set of Ford circles in terms of triples of relatively prime integers that satisfy a certain equation. This is interesting because we have developed a better approximation for irrational numbers between 0 and 1 and because our new parameterization generalizes to a higher dimension.

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