Akhmim Wooden Tablet

The Akhmim wooden tablets or Cairo wooden tablets (Cairo Cat. 25367 and 25368) are two wooden writing tablets dating from ancient Egypt. They each measure around 18 by 10 inches and are covered with plaster. The tablets are inscribed on both sides. The hieroglyphic inscriptions on the first tablet include a list of servants, which is followed by a mathematical text. The text is dated to year 38 (it was at first thought to be from year 28) of an otherwise unnamed king. The general dating to the early Egyptian Middle Kingdom combined with the high regnal year suggests that the tables may date to the reign of the 12th dynasty pharaoh Senusret I, ca. 1950 BC. The second tablet also lists several servants and further contains mathematical texts.

The tablets are currently housed at the Museum of Egyptian Antiquities in Cairo. The text was reported by Daressy in 1901 and later analyzed and published in 1906.

The first half of the tablet details five multiplications of a hekat unity (64/64) by 1/3, 1/7, 1/10, 1/11 and 1/13. The answers were written in binary Eye of Horus quotients, and exact Egyptian fraction remainders, scaled to a 1/320 factor named ro. The second half of the document proved the correctness of the five division answers by multiplying the two-part quotient and remainder answer by its respective (3, 7, 10, 11 and 13) dividend that returned the ab initio hekat unity, 64/64.

In 2002, Hana Vymazalová obtained a fresh copy of the text from the Cairo Museum, and confirmed that all five two-part answers were correctly checked for accuracy by the scribe that returned a 64/64 hekat unity. Minor typographical errors in Daressy's copy of two problems, the division by 11 and 13 data, were corrected at this time. The proof that all five divisions had been exact was suspected by Daressy, but was not proven in 1906.

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