Monday, May 14, 2007

The Ahmes code

"The Egyptians needed fractions to divide food and supplies according to specific ratios. Fractions were so important that of the 87 problems in the Ahmes Papyrus only six did not involve them. Likewise, of the 25 problems in the Moscow Papyrus 22 involved calculations with fractions. Because the Egyptians performed multiplications and divisions by doubling and halving, it was necessary to double fractions too. Scribes created tables of calculations of fractions along with integers. These tables would be used as references, so that the chief of personnel could carry out the fractional divisions on site. With the exception of the frequently-used fraction 2/3, and the less frequent 3/4, a scribe, being asked to divide an object into a certain number of pieces, would express his fractions as a sum of unit fractions, i.e. limiting them mainly to fractions of the form 1/n where n is a positive integer. Mathematicians call these types of fractions Egyptian Fractions and request, as Ahmes did, that the unit fractions be distinct. A unit fraction is represented in hieroglyphic numerals by placing a mouth, which meant "part", above the number."
Ouch! My brain hurts. See the above page for the rest of this fascinating article by Assem Deif .

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