Ancient Egyptian Lives (AEL)


Mathematics




Most of what is known of Egyptian Mathematics derives from a small amount of papyri that were compiled as pratical textbooks for the training of scribes at an advanced level of education. Our knowledge is derived from the following sources:

  • "Rhind Papyrus" - A papyrus dated to the time of King Auserre-Apepa, a Hyksos king, and purporting to have been copied from a document of the time of King Amenemhet III.
  • "Moscow Papyrus" - Of the Middle Kingdom; still partly unpublished.
  • "Kahun Fragments" - Portions of 12th dynasty papuri.
  • "The Mathematical Papyrus from Akhmim" - Dating to between the sixth and the ninth centuries A.D.
  • "Anastasi Papyrus I" - A long satirical letter showing how to calculate the number of bricks required for a sloping embankment with a batter and with internal compartments, and to determine the weight of an obelisk.
  • A Middle Kingdom papyrus, now in Berlin.
  • Two wooden tablets, of the Middle Kingdomm in the Cairo Museum (Cat. no. 25367/8)
  • A Demotic papyrus of the Roman Period, containing tables of fractions.
  • Several tables of fractions of Byzantine date.
  • A Coptic ostrakon with tables of fractions.

  • The Egyptian's use of math was more pratical than anything else, and used through out daily life. Listed below are some of the ways in which math was used:

  • Calculation of crop yields in relation to land areas
  • Food commodities against consumption rates
  • Input of labour and raw materials for work projects and the running of temples

  • The hieroglyphic decimal system that the Ancient Egyptians used had separate symbols for the numbers 1, 10, 100, 1,000 and 10,000(as can be seen in the graphics above), also there was no symbol for zero. Intermediate numbers were written as multiples of the single number. All mathematical procedures were based on the underlying processes of addition and subtraction.

  • Multiplication - Was got by adding a number to itself the requisite number of times.
  • Division - Was obtain by subtracting a number until an indivisible remainder was left.
  • As it seems, there are no traces of the use of multiplication tables. Although the multiplication and division of by ten was a standard pratice. The process for fractions was based on the addition and subtraction of unit fractions. In exception to the special cases of 2/3 and very rarely 3/4, the Egyptians did not use multiples of fractions, but only the single unit fration.

    A great example of egyptian mathematics at work:

    The Army scribe, Amenemope, was challenged to calculate the number of men that would be needed to transport an obelisk of given size from the quarries, to errect a colossus in a given time, calculate the rations necessary to feed men digging a lake, and to arrange stores for a major military expedition to Syria.

    The Egyptian system of notation was decimal. It was in the manner in which fractions were expressed that the Egyptian system of notation shows such peculiar features, rendering their method of calculation so very different from ours. A fraction was represented by writing the mouth-sign, probably reading ro and meaning 'a part', above the number which we should describe as the denominator. In Egyptian, the number following the word ro had an ordinal meaning, and ro/5 means 'part five' or the 'fifth part', which concludes a row of equal parts together constituting a single set of five. As being the part which concluded the row into one series of the number indicated, the Egyptian ro-fraction was necessarily a fraction with, as we should say, unity as the numerator. To the Egyptian mind it would have seemed nonsense and self-contradictory to write ro 4/7, for in any series of seven, only one part could be the seventh, namely, that which occupied the seventh place in a row of seven equal parts laid out for inspection. The Egyptians, though he must have been able to realize, for example, what four parts out of seven meant, had to express 4/7 as 1/2 + 1/14; similarly, 11/49 had to be expressed as 1/7 + 1/14 + 1/98, or by other aliquot fractions giving the same sum.

    Weights and Measures

    The basic Egyptian unit of length measurement was the "royal cubit"(about 20in or 50cm), consisting of seven "palm-widths"(3in or 7.5cm), each of four "finger-widths"(3/4in or 1.9cm). The standard cubit, based on the distance between elbow and fingertips, was six palm-widths. One hundred cubits made one khet. The standard land measure was a setjet (usually referred to by the Greek equivalent, an aroura), consisting of one hundred square cubits (about 2/3 of an English acre or just over 0.25ha). Measures for grain were the hekat (just over a gallon or five litres), made up of ten hin; a quadruple hekat, often called an oipe(t); and a khar, or sack of four oipe(t) (17 gallon or 80 litres). Liquid was normally measured by the hin (approximately one pint or 0.5 litres). The standard measure of weight was the deben (two pounds or 0.9kg), divided into ten qite, or at some periods divided into twelve shat.


    Click here to go back to Main Menu.

    Copyright by Ancient Egyptian Lives ©1997-99, All Rights Reserved.