Akhmim Wooden Tablet

The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt Museum in Cairo.

The document was believed for nearly 100 years to define a unit known as a "ro" as being equal to 1/320th of a hekat, when in fact an exact computation was taking place that requires no additional units of the hekat. The "ro" operation was simply 5/320=1/64 as used to exactly complete the remainder fraction component of the following divisions:

64/3=21+1/35/(3 ro) = 5/960
64/7=9+1/75/(7 ro) = 5/2240
64/10=6+2/510/(10 ro) = 1/320
64/11=5+9/1145/(11 ro) = 45/3520
64/13=4+12/1360/(13 ro) = 60/4160

The student scribe was then asked to prove his/her division by multiplying by 3, 7, 10, 11, 13, as required, to find the complete 1/64th unit. Since the student compiling this tablet made many arithmetic errors in the duplication arithmetic, even a 2002 translation of the document did not fully recognize the exact nature of all the division operations. The Rhind papyrus also contains one of these problems, division by 3, leading to confusion by Gillings (1972) and others.

The importance of the tablet is that the system of Egyptian fractions may have originated in trying to divide the smallest grain units or some other units in ancient Egyptian history.

See also

Egyptian Fraction, Egyptian Mathematical Leather Roll, Rhind Papyrus

This entry contributed by Milo Gardner

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Daressy, G. "Cairo Museum des Antiquities Egyptiennes." Catalogue General Ostraca, Volume No. 25001-25385, 1901.Gillings, R. Mathematics in the Time of the Pharaohs. Boston, MA: MIT Press, pp. 202-205, 1972.Peet, T. E. "Arithmetic in the Middle Kingdom." J. Egyptian Arch. 9, 91-95, 1923.Vymazalova, H. "The Wooden Tablets from Cairo: The Use of the Grain Unit HK3T in Ancient Egypt." Archiv Orientalai, Charles U., Prague, pp. 27-42, 2002.

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Akhmim Wooden Tablet

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Gardner, Milo. "Akhmim Wooden Tablet." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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