Ahmes (more accurately Ahmose) was an Egyptian scribe who lived during the Second Intermediate Period. A surviving work of Ahmes is part of the Rhind Mathematical Papyrus now located in the British Museum (Newman, 1956). Ahmes states that he copied the papyrus from a now-lost Middle Kingdom original, dating around 1650 BC. The work is entitled directions for knowing all dark things and is a collection of problems in arithmetic, algebra, geometry, weights and measures, business and recreational diversions. The 51 member 2/nth table and the following 84 problems were presented with solutions. But, the scribe only offered brief notes citing the why and how of his often hard to read steps. However, bringing in additional documents like the Akhmim Wooden Tablet, Egyptian Mathematical Leather Roll, Reisner Papyrus and the Moscow Mathematical Papyrus a broader view of Ahmes's math is being found. For example, the 2/nth table can be seen as generally writing 1/p, 1/pq, 2/p, 2/pq and higher vulgar fractions into exact Egyptian fractions using standard methods. On a broader level, considering the RMP and its parent dcouments the Egyptian fraction notation was birthed around 2,000 BCE, most likely as a method to replace the Old Kingdom's binary fraction Horus-Eye notation, and its awkward round off system. Finally, considering the connections provided by all the Middle Kingdom texts, the why's and how's of the mathematics that Ahmes drew upon is finally coming into focus. Ahmes' methods, as taught to him, and followed by later scribes always wrote vulgar fractions in exact ways, never rounding off when rational numbers were involved. ame meaning The Moon is born or Child of the Moon. It was very popular in the beginning of the eighteenth dynasty. ... The Second Intermediate Period marks a period when Ancient Egypt once again fell into disarray between the end of the Middle Kingdom, and the start of the New Kingdom. ... The Rhind Mathematical Papyrus ( papyrus British Museum 10057 and pBM 10058), is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. ... The British Museum in London, England is one of the worlds greatest museums of human history and culture. ... Papyrus plant Cyperus papyrus at Kew Gardens, London Papyrus is an early form of paper produced from the pith of the papyrus plant, Cyperus papyrus, a wetland sedge that was once abundant in the Nile Delta of Egypt. ... The Middle Kingdom is: a old name for China a period in the History of Ancient Egypt, the Middle Kingdom of Egypt This is a disambiguation page — a navigational aid which lists pages that might otherwise share the same title. ... (Redirected from 1650 BC) Centuries: 18th century BC - 17th century BC - 15th century BC Decades: 1690s BC 1680s BC 1670s BC 1660s BC - 1650s BC - 1640s BC 1630s BC 1620s BC 1610s BC 1600s BC Events and trends Egypt: Start of Seventeenth Dynasty Significant people Categories: 1650s BC ... The Akhmim Wooden Tablet, is an ancient Egyptian artifact that has been dated to 2000 BC, near to the beginning of the Egyptian Middle Kingdom. ... The Egyptian Mathematical Leather Roll (also referred to as EMLR) was a 10 x 17 leather roll purchased by Alexander Henry Rhind in 1858. ... THE REISNER PAPYRUS is one of the most basic of the hieratic mathematical texts. ... The Moscow and Rhind Mathematical Papyri are two of the oldest mathematical texts discovered. ...

Yet, there were times when Ahmes did round off. Ahmes states without proof that a circular field with a diameter of 9 units is equal in area to a square with sides of 8 units (Beckmann, 1971). This method shows that Ahmes tried to 'square a circle', rather than using our modern Greek definition of the area of a cicle: pi*r^2. In modern notation Ahmes' method wrote out:

π(9/2)² = 8²

This method leads to a value of pi approximately equal to 3.16, within two hundreths of the true value of pi. This irrational number pi approximation reached beyond the rational number domain of Egyptian mathematics, but failed,as anyone would at any time, when compared to modern standards of approximations. This early approximation of pi was consistently used to compute the volume of a hekat, and its many sub-units, including the hin, ro, and dja as recorded in the RMP, Akhmim Wooden Tablet and 2,000 later medical prescriptions reported in the medical texts, information that 2002 work by Tanja Pemmerening and others have been reporting after 2001 as new metrological interpretations of the ancient texts, finally being able to translate the information in modern scaled units of measure. When a circles diameter is 1, its circumference is π. The mathematical constant π is an irrational real number, approximately equal to 3. ... When a circles diameter is 1, its circumference is π. The mathematical constant π is an irrational real number, approximately equal to 3. ... A hekat is an ancient Egyptian weights and measures volume unit, used to measure grain, bread, and beer, and further sub-divided into other units for medical prescriptions, beginning with the oipe, hin, jar, dja and ro. ... The Akhmim Wooden Tablet, is an ancient Egyptian artifact that has been dated to 2000 BC, near to the beginning of the Egyptian Middle Kingdom. ...

References

• Reisner Papyrus, http://reisnerpapyri.blogspot.com
• Ahmen. University of St. Andrews on Guido Castelnuovo. Retrieved on 2 October, 2005.
• Beckmann, Petr (1971). A History of PI. New York:St. Martin's Press.
• Newman, James R. (1956). The World of Mathematics; Volume 1.
• Pemmerening, Tanja, "Altjioagyptische Holmasse Metrologish neu Interpretiert" and relevant phramaceutical and medical knowledge, an abstract, Phillips-Universtat, Marburg, 8-11-2004, taken from "Die Altagyptschen Hohlmass" in studien zur Altagyptischen Kulture, Beiheft, 10, Hamburg, Buske-Verlag, 2005