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Square Representation of Farey Sequences

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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 .

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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 .

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Contributed by: Carlos Enrique Nosa Guzman (August 2022)
Open content licensed under CC BY-NC-SA

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This Demonstration is based on [1, Chapter 1].

Reference

[1] A. Hatcher, Topology of Numbers, New York: Cornell University, 2018.

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