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.
Sources
- 1801: Charles Haros: Tables 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 Farey: On a Curious Property of Vulgar Fractions (Phil. Mag. Vol. 47, no. 3: pp. 385 – 386)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Farey sequence (of order $n$)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Farey sequence (of order $n$)