Friday, July 5, 2013

RMP 2/n table

BREAKING the RMP 2/n Table CodeAuthor Breaking the RMP 2/n table code has been an important project for historians. By decoding scribal 2/n table methods scholars are learning 1650 BCE and earlier arithmetic methods. In 2006 and 2011 scribal thinking was broken and confirmed by demonstrating that rational numbers n/p were always scaled to mn/mp. The conclusion was reached by decoding every line and shorthand note recorded by the scribe Ahmes in . The attested scribal  methodology selected  the best least common multiple (LCM) m before red auxiliary numbers, divisors of denominators mp, were recorded in concise unit fraction series.During the 19th, 20th and 21st centuries the hard-to-read scribal shorthand was required to be parsed by looking for omitted initial and intermediate steps. Peet applied the Latin name "" to denote required and proposed studies, the last of which may be the above 2006 and 2011 studies. Scribal shorthand did not reveal pertinent scribal details nor needed decoding keys easily.. The hieratic unit fraction system was proposed to anticipate modern finite arithmetic by F. Hultsch in 1895. Hultsch's suggestion was confirmed by , but usually ignored by the larger scholarly community. Several 20th century scholars also proposed finite arithmetic and number theory as decoding keys to read aspects of  scribal arithmetic. For example, .By 2006, attested historical details began to appear. The actual scribal facts were parsed by adding back actual missing initial and intermediate factual steps mentioned in RMP 36. Fully decoding RMP 36  and other RMP problems in historical context have exposed previously unknown scribal encoding keys.By 2011, using the new decoding keys it is clear that a LCM m method was used by Ahmes that facilitated conversions of  rational number n/p in a multiplication context. that may soon end the 1879 to 2011 debate.The paper describes hieratic arithmetic that scaled n/p by m/m to mn/mp in steps that allowed Ahmes to inspect the divisors of denominator mp for the purpose of listing the best set of divisors that summed to numerator mn. Red numbers were used by Ahmes to denote the importance of the additive set of divisors that summed to mn. Ahmes then wrote out concise unit fraction series representations of rational numbers n/p within a scribal method that considered number theory (that were close to F. Hultsch's  117 year old, and Kevin Brown's 17 year old suggestions).Scribes like Ahmes outlined the information in once hard-to-read shorthand notes.  Ahmes' notes revealed that LCM m method selected the best divisors of denominator mp summed in red auxiliary numbers to mn. Breaking the 2/n table code is allowing all 87 RMP problems to be decoded as well as other Middle Kingdom mathematical text problems.In retrospect, the resultant Egyptian fraction system was reported in 2006 and 2011 by showing that concise unit fraction series had corrected an Old Kingdom Horus-Eye binary infinite series notation reported as:1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64+ ...

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