On approximating irrational numbers as fractions (algorithms)

Rational numbers are easy. But they are far outnumbered by irrationals. These beasts of infinitely-long decimal expansions take the vast majority of the infinity of real numbers. But we can't compute their exact values, so we use the next best thing - an approximation.

This is a companion discussion topic for the original entry at https://kblagoev.com/blog/on-approximating-irrational-numbers-as-fractions-algorithms/