Hekat (volume unit)

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A hekat is an ancient Egyptian weights and measures volume unit, used to measure grain, bread, and beer. It was further sub-divided into other units for medical prescriptions, beginning with the oipe, hin, jar, dja and ro. The hin was a 1/10th of a hekat unit, while the ro was a 1/320th of a hekat unit. The dja was recently evaluated by Tanja Pemmerening in 2002, greatly improving the readability of the medical texts. In addition, Hana Vymazalova evaluated the hekat in 2002 from Akhmim Wooden Tablet, dividing it by small numbers, again, greatly improving its readability.

The hekat was also found is the Rhind Mathematical Papyrus, and many other texts, including the Ebers Papyrus, the best known medical text. This volume unit was defined in the Moscow Mathematical Papyrus by MMP #10, by approximating pi to around 3.16. The approximation of pi was achieved by squaring a circle, increasingly (i.e. for the denominator in terms of setats: 9, 18, 36, 72, and 81, Gillings, page 141) until the vulgar fraction 256/81 was reached, the only relationship that was used in the Egyptian Middle Kingdom. The MMP scribe then found the surface area of a basket = (8d/9)^2 = 64d^2/81 as a cylinder relationship to the hekat, meaning that d = 2 may have defined a hekat or 256/81, the exact number used to approximate pi. The ancient Egyptian weights and measures discussion further shows that the hekat was 1/30th of a royal cubit^3, an analysis that needs to double checked, against the d = 2 suggestion, which means that r = 1, a suggestion that does make sense.

[edit] References

Gillings, Richard. "Mathematics in the Time of the Pharaohs" Dover, reprint from, Cambridge, Mass, MIT Press 1972, ISBN 0-486-24315-X.

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.