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Partitioned Trapezoid
”IM 58045…is a round mathematical hand tablet securely dated to the Old Akkadian period (five hundred years before the Old Babylonian period), since it was found in the ruins of a collapsed house together with explicitly dated administrative documents [reign of King Šarkališarri]. The diagram on the obverse…shows a trapezoid divided into two parallel stripes by a transversal parallel to the fronts of the trapezoid. The two fronts are given as 3 reeds - [1 cubit] and 1 reed 1 cubit, respectively. Since 1 reed = 6 cubits, this means that the fronts are 17 and 7 cubits. The length (or height) of the trapezoid is given as 2 reeds = 12 cubits (= 1 ninda). Consequently, the area of the whole trapezoid is
A = 12 cubits · (17 cubits + 7 cubits)/2 = sq. (12 cubits) = 1 sq. ninda = 1 sar.” - Jöran Friberg, A Geometric Algorithm with Solutions to Quadratic Equations in a Sumerian Juridical Document from Ur III Umma, §9.3.1 Cuneiform Digital Library Journal 2009:3
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Original Text and Translation
”It is likely that the diagram…was an assignment, in the sense that a school boy took the hand tablet with the diagram with him home from school one day and was expected to return to school the next day, handing in to the teacher the solution to the trapezoid bisection problem with the data recorded on the hand tablet.” Ibid., §9.4.
Nippur mathematics teacher’s golden [?] problem selection:
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Dr. Troglodyte
