| Abstract [eng] |
Farey sequences are named after the British geologist John Farey, whose letter about these sequences was published in the Philosophical Magazine in 1816. Farey conjectured that each term in a Farey sequence is the mediant of its neighbours. In this work you may find the analysis of the main properties of Farey sequences, different their interpretations, examples. Also there is considered the question of the aproximation of real number by Farey sequence. Various situations and a few algoritms (Farey sequence formation, Ford circles drawing) were demonstrated using MAPLE. These and others facts introduce the Farey sequences as picturesque mathematical object. |
