Some Characteristics of the Farey Sequences with Ford Circles

Authors

  • Bal Bahadur Tamang Department of Mathematics, Mahendra Ratna Multiple Campus, Ilam, Tribhuvan University, Nepal
  • Shes Raj Kumar Sharma Department of Mathematics, Bhairahawa Multiple Campus, Tribhuvan University, Nepal
  • Sita Laxmi Lawaju Central Department of Mathematics,Tribhuvan University, Kirtipur, Kathmandu, Nepal
  • Ajaya Singh Central Department of Mathematics,Tribhuvan University, Kirtipur, Kathmandu, Nepal

DOI:

https://doi.org/10.3126/njmathsci.v4i1.53159

Keywords:

Farey sequence, Irrational number, Mediant, Approximation, Ford circle, Hurwitz Theorem

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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Published

2023-04-04

How to Cite

Tamang, B. B., Sharma, S. R. K., Lawaju, S. L., & Singh, A. (2023). Some Characteristics of the Farey Sequences with Ford Circles. Nepal Journal of Mathematical Sciences, 4(1), 69–76. https://doi.org/10.3126/njmathsci.v4i1.53159

Issue

Vol. 4 No. 1 (2023)

Section

Articles

License

© School of Mathematical Sciences, Tribhuvan University