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Farey Sequence & Ford Circles

The Farey sequence Fn contains all fractions p/q with 0 ≤ p/q ≤ 1 and q ≤ n, in ascending order.

Ford circles: Each fraction p/q has a circle of radius 1/(2q²) tangent to the x-axis at x = p/q.

Mediant: a/b ⊕ c/d = (a+c)/(b+d)

Adjacent Ford circles are always tangent to each other!

Fraction

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