# Ford Circles

Ford Circles

The Farey sequence for a positive integer is the set of irreducible rational numbers with and . For example, is , ,,,,,. The Ford circle has radius and center ,. It is tangent to the x axis at and to the circles corresponding to the two neighbors of in .

F

n

n

h

k

0≤h≤k≤n

(h,k)=1

F

4

0

1

1

4

1

3

1

2

2

3

3

4

1

1

C(h,k)

1

2

2

k

h

k

1

2

2

k

h

k

h

k

F

n