Dating directrix

20-Apr-2020 12:47 by 5 Comments

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The texts that survive do not reveal what, if any, special procedures the scribes used to assist in this.

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Using the same table as in the multiplication problem, one can see that 8 produces the largest multiple of 28 that is less then 308 (for the entry at 16 is already 448), and 8 is checked off.The entire process is analogous to the process of solving the algebraic equation for the problem (circle (Rhind papyrus, problem 50): 1/9 of the diameter is discarded, and the result is squared.For example, if the diameter is 9, the area is set equal to 64.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).(In most cases, of course, there is a remainder that is less than the divisor.) For larger numbers this procedure can be improved by considering multiples of one of the factors by 10, 20,…or even by higher orders of magnitude (100, 1,000,…), as necessary (in the Egyptian decimal notation, these multiples are easy to work out).

Thus, one can find the product of 28 by 27 by setting out the multiples of 28 by 1, 2, 4, 8, 10, and 20.

The information comes primarily from two long papyrus documents that once served as textbooks within scribal schools.

The Rhind papyrus (in the British Museum) is a copy made in the 17th century , presents 25 problems of a similar type.

(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).

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.

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