Noun
Ford circle (plural Ford circles)
(geometry) Any one of a class of circles with centre at (p/q, 1/(2q)) and radius 1/(2q), where p/q is an irreducible fraction (i.e., p and q are coprime integers).
Every Ford circle is tangent to the horizontal axis
y
=
0
{\displaystyle y=0}
, and any two Ford circles are either disjoint or meet at a tangent.
There is a unique Ford circle associated with every rational number. Additionally, the axis
y
=
0
{\displaystyle y=0}
can be considered a Ford circle with infinite radius, corresponding to the case
p
=
1
,
q
=
0
{\displaystyle p=1,\ q=0}
.