Pick any two Integers and , then the Circle of Radius centered at
is known as a Ford circle. No matter what and how many s and s 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 and ,

(1) |

(2) |

(3) |

**References**

Conway, J. H. and Guy, R. K. ``Farey Fractions and Ford Circles.'' *The Book of Numbers.* New York:
Springer-Verlag, pp. 152-154, 1996.

Ford, L. R. ``Fractions.'' *Amer. Math. Monthly* **45**, 586-601, 1938.

Pickover, C. A. ``Fractal Milkshakes and Infinite Archery.'' Ch. 14 in *Keys to Infinity.* New York:
W. H. Freeman, pp. 117-125, 1995.

Rademacher, H. *Higher Mathematics from an Elementary Point of View.* Boston, MA: Birkhäuser, 1983.

© 1996-9

1999-05-26