Egyptian Fraction Decomposer

About this calculator

An Egyptian fraction expresses a proper fraction as a sum of distinct unit fractions — fractions with numerator 1, like 1/2 + 1/3 + 1/10 — the form ancient Egyptian mathematicians used (as recorded in documents like the Rhind Mathematical Papyrus) since their numeral system had no convenient way to write general fractions such as 2/5.

This decomposer uses the greedy algorithm, sometimes called the Fibonacci–Sylvester method after Fibonacci's 13th-century description and Sylvester's 19th-century proof that it always terminates: at each step it subtracts the largest unit fraction not exceeding the remaining value, then repeats on the remainder. The result is always a finite sum of distinct unit fractions, though not necessarily the shortest one possible — a genuinely open problem for some fractions is finding the minimum number of terms.