08 Feb '13 14:05

Egyptians had a number system that had no fractions the way we know them. Instead, they used integers, and the inverse numbers of integers. To express other fractions, they used sums of inverse numbers of integers, and to make it even more challenging, required that the sums did not involve duplicates. Eventually the number system evolved the include a symbol for 2/3. I've heard it said that this peculiar kind of math kept Egyptian priests in power for thousands of years as only they knew how to do fractions like that, and math was not allowed to get easier so as to keep others from taking the jobs. I've also heard that this was one of the more important reasons about why the Egyptians managed to build the pyramids, and very little after that for the next couple of millenniums until the Romans came.

Thus, for example Egyptians wrote 3/4 as 1/2 + 1/4; and 7/12 as 1/3 + 1/4.

Questions are..

* how do you write 2/3 as a sum of different inverse numbers?

* is there a method to write any fraction m/n as a sum of inverse numbers?

Thus, for example Egyptians wrote 3/4 as 1/2 + 1/4; and 7/12 as 1/3 + 1/4.

Questions are..

* how do you write 2/3 as a sum of different inverse numbers?

* is there a method to write any fraction m/n as a sum of inverse numbers?