Modern scholars have encountered difficulties finding the context from which Egyptian fractions were first created. Egyptologists assumes that the all of the origins of the unit fraction system began in the Old Kingdom. Aspects of it did, solving an Old Kingdom binary round-off problem. Math historians tend to read the Middle Kingdom math texts as independent documents, allowing the mathematical information considered by the personal views of researchers to determine the direction of the research. How can personalized and conflicting points of view be resolved?

One way is to show that Old Kingdom binary number numeration system was built upon a numeration system that rounding off to six binary fraction terms. Old Kingdom scribes worked to resolve round off problem. Only in the Middle Kingdom were the binary round off problems corrected. A finite rational number system burst onto the Middle Kingdom stage. Scribes, such as Ahmes, used a new cipher numerations system to record Egyptian fraction mathematics, beginning with modern-like arithmetic definitions of addition, subtraction, multiplication and division, hidden beneath the "Russian Peasant" type of Old Kingdom algorithmic multiplication operation.

In other words, jumping to the present era, the formal research of reading the most important Egyptian mathematical document, the Rhind Mathematical Papyrus (RMP), began in 1879, with the mulling over of the 'best' meaning and 'first' use of the 2/nth table. One of the most prepared of the modern mathematicians that have taken time to research this topic is Kevin Brown. Brown published his work on the internet around 1995. Like those those mathematicians that had gone before him, Brown inspected several elements of the 2/nth table. Concerning the critical element of the 'first' uses of Egyptian fractions, Brown seeing many exact mathematical statements in the 2/nth table, he offered the suggestion that the ancient scribes may have been gamblers

a point of view that is historically incorrect.

Egyptian fraction math was created as a means to decentralize the Egyptian economy.

The majority of the earlier scholars offered less insightful conclusions concerning the first 'uses' of Egyptian fractions. For example, the interesting 2/nth table patterns, as used to exactly solve many of the 87 RMP problems, have not been formally resolved in academic journal debates.

Traditional math history scholars have failed to parse Ahmes 2/n table construction methods for several reasons, the main barrier being the consideration of the additive aspects of the unit fraction series. Well motivated scholars muddle the essence of Ahmes 87 problems, by not reading every line of Ahmes rational number scaling method --- described in RMP 36 and RMP 37.

## Wednesday, May 10, 2006

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