Egyptian Fractions

The Egyptian were a clever lot. They discovered a lot of science/math out of necessity and availability of many strange phenomena. The flooding valley of the Nile left them with really fertile ground and gave them several opportunities. Having a large amount of the valley area flood every year fomented community organization and the establishment of a city authority to delegate zoning. Grain surpluses translated in hyperaccelerated development and trade.

The grain trade led to the creation of a set of measurements and instruments. One popular unit was the Heqat that measured volume. You would go to a bar in Men-nefer (Memphis) sit between the sun priest and the scribe and order 1/5 Heqat (1pint) of fine Egyptian beer which you would drink through a straw.

Out of the grain trade arose the necessity to create a system of fractional numbers. since grain could not be sold by the number a heqat was determined to be an important unit and any fraction of it would be represented as a sum of unit fractions. this was likely due to having to carry a different set of containers that could measure each fractional ammount.

so an egyptian merchant would have his heqat bag, a half heqat bag a third heqat bag a fourth heqat bag a fifth heqat bag....
so they decided to represent numbers as sums of unit fractions.

			(2)
			(3)
			(4)
			(5)
			(6)
			(7)
			(8)
			(9)
			(10)

if you were an important egyptian mathematician and wanted to know the value of pi.you would make using a compass you draw a circle in the ground with one cubit of radius.
then the egyptian representation of pi would be
3 + 1/8 + 1/61 + 1/5020 +1/128541455 + 1/162924332716605980
this number system only has one advantage to reduce the number of bits necessary to express common units like 1/2 or 1/4 or 3/4 or 2/3.

Perhaps it was this awefull system that plateaued egyptian mathematical progress and let the summerians and other civs improve much more.