A Ford circle is a geometric construct that is used in number theory to visually represent the fractions between 0 and 1. Specifically, for each positive fraction \( \frac{p}{q} \) (where \( p \) and \( q \) are coprime integers), the corresponding Ford circle is centered at \( \frac{p}{q} \) with a radius of \( \frac{1}{2q^2} \).
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