Mark Chu Carroll over at the Good Math, Bad Math blogs has a fascination with bizarre bits of math as I do. Today, he had a post about something which I investigated quite a bit a number of years ago: so-called Egyptian Fractions. The ancient Egyptians had a peculiar way of representing fractional numbers. They always represented values as the sum of fractions with 1 in the numerator. Hence, if you were trying to represent 3/4, you’d instead write that as 1/2 + 1/4. Well, that doesn’t seem so hard. Let’s try to represent 2/3. A moment’s worth of thought might give you the expansion 1/2 + 1/6. How about 3/7?

It might take you a bit longer to come up with the expansion 1/3 + 1/14 + 1/42. Or maybe you got a different expansion, like 1/3 + 1/11 + 1/231. The fact is, these Egyptian fractions are a good deal more subtle than you might have imagined. There are numerous algorithms to try to generate interesting (mostly short) representations for arbitrary fractions: the best online reference that I’ve found (with plenty of code and information to chew through) is David Eppstein’s terrific page on Egyptian Fraction Algorithms.

[tags]Egyptian Fractions,Mathematics[/tags]