Снег. Keeps the dream alive.

Continued fractions cought my eye during Quantum Computation lectures where they have been introduced to prove the famous Shor's Algorithm, which for a number N, log N digits long, is able to output a factor 1 < K < N (or K = N if N is prime) in O(n^3) time. Yep, Shor's Algorithm is the one that made all bank security people suddenly go mad and extremely interested in Quantum Computing research.

Anyway, continued fractions is a beautiful way of representing rational and irrational numbers. Commonly used numbers such as 1/3 or 1/6 do not have a finite decimal representation which forces programmers to truncate them (i.e. cut off decimal part at a certain decimal place). Although, for most cases precision isn't necessary and even if 32-bit floating point number isn't enough, we always have a 64-bit floating point number we can use with almost no performance overhead on modern machines in general purpose programming. However, what if you want extra precision? What if you want to control how accurately a number is represented and want your result to be 100 rather than 99.99999. Then continued fractions are for you! Check out Wikipedia page for a definition. Also I stumbled across these lecture notes which give an overview of continued fractions arithmetic.