Ford circle

In mathematics, a Ford circle is a circle with center at ${\displaystyle (p/q,1/(2q^{2}))}$ and radius ${\displaystyle 1/(2q^{2}),}$ where ${\displaystyle p/q}$ is an irreducible fraction, i.e. ${\displaystyle p}$ and ${\displaystyle q}$ are coprime integers. Each Ford circle is tangent to the horizontal axis ${\displaystyle y=0,}$ and any two Ford circles are either tangent or disjoint from each other.

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