Small numerical variations in a set of similar problems from Nippur on the area of the square (Q2118258)

In Mesopotamia towards the end of the 3rd millennium BC, a place-value system with base 60 was invented. This allowed calculation much like our system with base 10. Tables for multiplication, squares, and reciprocals provided tools for calculations. Measures of length, area, volume and weight, however, had different relations between units. These were summarized in metrological tables, which transformed values of measurements into numbers in the sexagesimal system. All these tables had to be learnt by scribes during their education. The author investigates a group of six tablets found in Nippur which can be considered school exercises. Each gives an amount in length measure and asks for the area of a square with the given length. Because of the different factors between length measures, the square cannot be calculated immediately; the length had first to be converted into a sexagesimal number, whose square could be calculated by a known procedure (or looked up in a table). The square number had then to be converted into area measure by looking up the sexagesimal result in a table of area measures. Depending on the numbers, these conversions could be more or less complicated. The author follows the steps of these calculations in great detail so that the requirements for the student scribes become apparent for a modern reader. Each of the six tablets chosen by the author leads to different mental tasks to be performed. It is possible to arrange the tablets from the simpler to the more complicated. Therefore a pedagogical purpose of these exercises can hypothetically be inferred even it this is not mentioned in the texts.