Work out egyptian fraction instantly with clear inputs, formula shown and shareable results.
An Egyptian fraction writes a proper fraction as a sum of distinct unit fractions. Fibonacci's greedy algorithm repeatedly subtracts the largest unit fraction that fits, 1/⌈q/p⌉, and always terminates.
Greedy step
p/q = 1/⌈q/p⌉ + (p·⌈q/p⌉ − q)/(q·⌈q/p⌉)
The greedy algorithm gives 1/25 + 1/757 + 1/763309 + …, converging quickly to the exact value.
Their notation only had symbols for unit fractions (plus 2/3), so every quantity had to be expressed as a sum of them.