Wednesday 28 July 2021

The "Mediant" Series (aka "Farey" Series)

The Farey series gets its name from British geologist Farey.

It is notable that a geologist had such an impact on the theory of numbers.

In 1816, Farey published a statement that the middle of three successive terms is the "mediant" of the other two. 

The proof was supplied by Cauchy (or Baron Augustin-Louis Cauchy, to give him his full title).