WOLFRAM|DEMONSTRATIONS PROJECT

Ford Circles

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centerpoint

0.54

Farey depth

15

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The Farey sequence

F

n

for a positive integer

n

is the set of irreducible rational numbers

h

k

with

0≤h≤k≤n

and

(h,k)=1

. For example,

F

4

is

0

1

,

1

4

,

1

3

,

1

2

,

2

3

,

3

4

,

1

1

. The Ford circle

C(h,k)

has radius

1

2

2

k

and center

h

k

,

1

2

2

k

. It is tangent to the x axis at

h

k

and to the circles corresponding to the two neighbors of

h

k

in

F

n

.