Ford circle

The Ford circles are circles in the real plane, one each for each rational number and an infinity to the point. The circles are named after the American mathematician Lester R. Ford, who discovered them in 1938.

Definition

The Ford circle to break with relatively prime, integers, and is usually denoted by or. He is the radius and its center at the point. Also, the Ford circle is defined as the straight line ( a projective seen, this is a circle with the center at infinity ).

Properties of the Ford circles

The inside of each of two different Ford circles is disjoint, ie the circles do not overlap. However, they can touch each other. In addition, each rational point of x-axis is contacted by a Ford circuit.

If the break in the open interval, so the contact Ford circles correspond to just the neighbors in a Farey series.