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One of the texts popular as a copy exercise in the schools of the New Kingdom (13th century ) was a satiric letter in which one scribe, Hori, taunts his rival, Amen-em-opet, for his incompetence as an adviser and manager. But the point of the humour is clear, as Hori challenges his rival with these hard, but typical, tasks.“You are the clever scribe at the head of the troops,” Hori chides at one point, a ramp is to be built, 730 cubits long, 55 cubits wide, with 120 compartments—it is 60 cubits high, 30 cubits in the middle…and the generals and the scribes turn to you and say, “You are a clever scribe, your name is famous. What is known of Egyptian mathematics tallies well with the tests posed by the scribe Hori.
The geometric problems in the papyri seek measurements of figures, like rectangles and triangles of given base and height, by means of suitable arithmetic operations.(It is not as close, however, as the now common estimate of 3, first proposed by Archimedes, which is only about 0.04 percent too large.) But there is nothing in the papyri indicating that the scribes were aware that this rule was only approximate rather than exact.A remarkable result is the rule for the volume of the truncated pyramid (Golenishchev papyrus, problem 14).The scribe assumes the height to be 6, the base to be a square of side 4, and the top a square of side 2.He multiplies one-third the height times 28, finding the volume to be 56; here 28 is computed from 2 × 2 2 × 4 4 × 4.Since the entries 1, 2, 4, and 20 add up to 27, one has only to add up the corresponding multiples to find the answer.
Computations involving fractions are carried out under the restriction to unit parts (that is, fractions that in modern notation are written with 1 as the numerator).These elementary operations are all that one needs for solving the arithmetic problems in the papyri.For example, “to divide 6 loaves among 10 men” (Rhind papyrus, problem 3), one merely divides to get the answer 1/2 1/10. By virtue of their writing skills, the scribes took on all the duties of a civil service: record keeping, tax accounting, the management of public works (building projects and the like), even the prosecution of war through overseeing military supplies and payrolls.Young men enrolled in scribal schools to learn the essentials of the trade, which included not only reading and writing but also the basics of mathematics. This problem, and three others like it in the same letter, cannot be solved without further data.The scribe recognized that the area of a circle is proportional to the square of the diameter and assumed for the constant of proportionality (that is, π/4) the value 64/81.