Egyptian Fractions

The ancient Egyptians were known to write a fraction p/q as a sum of unit fractions. If all of them are different, they were called Egyptian fractions. The interesting thing is to find such a representation, particularly with regard to the number of fractions and the size of the denominators, which are often asked to be small.
For example, 10/13 can be written as 1/2 + 1/4 + 1/52, but the expansion 1/2 + 1/6 + 1/13 + 1/39 with smaller denominators is also possible.

The following applet allows you to find such Egyptian fractions (therefore Java must be installed). Input a fraction between 0 and 1, and you will shown an Egyptian expansion for it.

Links related to Egyptian Fractions

1. Ron Knott's web page gives a survey about some algorithms to find Egyptian Fractions.
2. The Wikipedia entry gives you some general information and further links.
3. If you like to study the mathematical background, you should visit David Eppstein's web page, which includes interesting links to scientific papers and current work.
4. An expansion table for fractions of the form 2/n, taken from the Rhind Papyrus.
5. A short narrative on PlanetMath.org.

Last modified: 05/12/2008