Definition:Farey Sequence/Historical Note

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Historical Note on Farey Sequence

The Farey sequence was first exploited by Charles Haros in $1801$ in creating tables of the decimal expansions for all vulgar fractions whose denominators are less than $100$.

In order to make sure he captured them all, he used a technique exploiting the properties of the mediant that originated with Nicolas Chuquet.

Some $15$ years later, John Farey rediscovered this property, and published a paper on the subject.

This was subsequently picked up on by Augustin Louis Cauchy, who reproved the results of Charles Haros while crediting John Farey with the technique.


  • 1801: Charles HarosTables pour évaluer une fraction ordinaire avec autant de decimals qu'on voudra; et pour trouver la fraction ordinaire la plus simple, et qui approche sensiblement d'une fraction décimale (J. l'École Polytechnique Vol. 6, no. 11: pp. 364 – 368)
  • 1816: John FareyOn a Curious Property of Vulgar Fractions (Phil. Mag. Vol. 47, no. 3: pp. 385 – 386)