Square Representation of Farey Sequences

The Farey sequence of order runs over all the irreducible rational numbers between 0 and 1 with denominator at most , constructed by the Farey addition of consecutive pairs of terms from the previous Farey sequence. The Farey addition of two given fractions and is defined as .

The diagram is based on the result that, if we construct a quadrilateral with vertices , , and , then the diagonal lines of this figure intersect at the point .