Date: Nov 4, 2012 10:31 AM
Author: Milo Gardner
Subject: Re: Why study Egyptian fraction math?

On a higher numeration level the finite hieratic system scaled rational numbers by least common multiple (LCM) m to optimized, but not optimal, unit fraction series. Middle Kingdom scribes scaled rational numbers to unit fraction series by the LCM that created a numeration system in the AWT and other hieratic texts. The Egyptian fraction numeration system ciphered counting numbers 1:1 onto hieratic sound symbols replacing an Old Kingdom hieroglyphic many-to-one system numbers written in rounded-off binary numbers. A line was drawn over hieratic sound symbols to denote unit fractions. Carl B. Boyer reported the significance of the ciphered numeration system. Egyptian fraction series represented rational numbers in ordered unit fraction series, writing the smallest to the largest unit fraction, from left to right.

One purpose of the Egyptian fraction system involved a finite weights and measures system applied to a commodity based monetary system established by Pharaoh. One theoretical aspect of the monetary system contained Egyptian multiplication and division operations. The scribal arithmetic was undervalued by historians for over 120 years, from 1879 to 1999, by only reporting the additive aspects of the raw transliterated data.

Scribal unit fraction answers contained two sides, additive numerators, and LCM scaled reminders. Math historians, beginning with F. Hultsch in 1895, parsed aspects of the scribal aliquot part views of numerators and LCM denominators, though the unified aspects of the system remained vague for another 105 years. In 2002, the EMLR was validated containing aliquot parts of LCM denominators in none optimized manners. The LCM (m/m) was written as a unity becoming a multiplier that scribes used to scale rational numbers to optimized, but not optimal, unit fraction series in 2/n table tables and every day problem and answers. In 2006 the Akhmim Wooden Tablet was validated containing exact quotient and remainders within its primary division division method, an ancient fragment also documented in the RMP 2/n table in 2011.