This is cool if you're a math geek.
While I was researching yesterdays post on Archimedes integration, one of the things I read reminded me of one of the stranger things about Greek and earlier math. They had a notion that the only valid fractions were unit fractions; that is, fractions whose numerator is 1. A fraction that was written with a numerator larger than one was considered wrong. Even today, if you look in a lot of math books, they use the term "vulgar fraction" for non-unit fractions.
Obviously, there are fractions other that 1/n. The way that they represented them is now known as Egyptian fractions. An Egyptian fraction is expressed as the sum of a finite set of unit fractions. So, for example, instead of writing the vulgar fraction 2/3, the Greeks would write "1/2 + 1/6".
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We don't know that much about the origins of Egyptian fractions. What we do know is that the earliest written record of their use is in an Egyptian scroll from roughly the 18th century BC, which is why they're known as Egyptian fractions.
That scroll, known as the Rhind Papyrus is one of the most fascinating things in the entire history of mathematics. It appears to be something along the lines of a textbook of Egyptian mathematics: a set of questions written roughly in the form of test questions, and fully worked answers. The scroll includes tables of fractions written in unit-fraction sum form, as well as numerous algebra (in roughly the equational reasoning form we use today!) and geometry problems. From the wording of the scroll, it's strongly implied that the author is recording techniques well-known by the mathematicians of the day, but kept secret from the masses. (What we would call mathematicians were part of the priestly class in Egypt, usually temple scribes. Things like advanced math were considered a sort of sacred mystery, reserved to the temples.)
Mathematicians were part of the priestly class? Cool!