Mathematics
The Farey Sequence and Rational Approximation to Irrationals
Quick fact
In the Farey sequence of order n, any two consecutive fractions a/b and c/d satisfy bc – ad = 1, a property that ensures every irrational number can be approximated by a Farey fraction with error less than 1/d², where d is the denominator.
Why this is interesting
Imagine you want to approximate the square root of 2 as a simple fraction. Where do you even start? The Farey sequence gives a surprisingly elegant way to find the best possible rational approximations with small denominators.