Three algorithms for Egyptian fractions

Abstract

The ancient Egyptians used a number system based on unit fractions, i.e. fractions with one in the numerator. This idea let them represent any fraction a/b as the sum of unit fractions e.g 27 = 14 + 128. Further, the same fraction could not be used twice (so 27 = 17 + 17 is not allowed). In this work we examine a number of algorithms for generating Egyptian fractions in more detail, implement them and analyze their performance.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 121-126