2023•Nepal Journal of Mathematical SciencesOpen access

Some Characteristics of the Farey Sequences with Ford Circles

Bal Bahadur Tamang, Shes Raj Kumar Sharma, Sita Laxmi Lawaju, Ajaya Kumar Singh

Abstract

Farey sequence is a pattern of rational numbers that approximates irrational numbers. In this paper, we use the Farey sequence to describe the Ford Circles. Its results and applications are equally fascinating as its pattern. Hurwitz Theorem is the main outcome of the approximation of irrational by rational numbers. Also, we examine the relationship between the Ford circle and the Farey sequence for rational values between 0 and 1.

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Key concepts: Farey sequence, Irrational number, Sequence (biology), Rational number, Mathematics, Combinatorics, Discrete mathematics, Geometry