Pick any two integers h and k, then the circle C(h,k) of radius centered at is known as a Ford circle. No matter what and how many hs and ks are picked, none of the Ford circles intersect (and all are tangent to the x-axis). This can be seen by examining the squared distance between the centers of the circles with (h, k) and
Let s be the sum of the radii
and the circles and intersect in
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Pickover, C. A. "Fractal Milkshakes and Infinite Archery." Ch. 14 in Keys to Infinity. New York: W. H. Freeman, pp. 117-125, 1995.
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