The beginning of Math

Made for 3MX

by

Jon Halvor Stridsklev og Jon Olav Hunderi

Egypt is known of its great contribution to the science of math. In the early years Egypt had several systems that made it easy to count, subtract and add numbers. The most known system is the hieroglyphic, which was a pictorial script where each character represented an object. Special symbols were used to represent each power of 10 from 1 to 10/7.

Multiplication and division were usually performed by a succession of doubling operations, based on the fact that any number can be represented as a sum of powers of 2. As an example of multiplication, let us find the product of 26 and 33. Since 26 = 16+8+2, we have merely to add these multiples of 33. The work may be arranged as follows:

Addition of the proper multiples of 33, that is those indicated by an asterisk, gives the answer 858. Again, you divide 753 by 26, we successively double the divisor 26 up to the point where the next doubling would exceed the dividend 753. The procedure is shown below:

Now, since

753 = 416 + 337

753 = 416 + 208 + 129

753 = 416 + 208 + 104 + 25

We see, nothing the starred items in the column above, that the quotient is 16+8+4=28, with a remainder of 25. This Egyptian process of multiplication and division not only eliminates the necessity of learning a multiplication table, but is so convenient on the abacus that it persisted as long as that instrument was in use, and even for some time beyond.

The dependence on unit fractions in arithmetical operations, together with the peculiar system of multiplication, led to a third aspect of Egyptian computation. Every multiplication and division involved unit fractions would invariably lead to the problem of how to double unit fractions. Now, doubling a unit fraction with an even denominator is simple matter of halving the denominator. Thus doubling ½, ¼, 1/6 and 1/8 yields 1, ½, 1/3 and ¼ . Doubling 1/3 raised no difficulty, for 2/3 had its own hieroglyphic symbol. But it was in doubling unit fractions with other odd denominators that difficulties arose. For some reason unknown to us, it was not permissible in Egyptian computation to write two times 1/n as 1/n + 1/n. Thus the need arose for some form of ready reckoned which would provide the appropriate unit fractions that summed to 2/n, where n= 5,7,9,…..

Ex:

2/5= 1/3 + 1/15

2/7= ¼ + 1/28

2/9= 1/6 + 1/18

Practical use of Egyptian maths

The Egyptians used geometry to calculate land areas and granary volumes. But Egyptians is doubtlessly mostly know for their pyramids. The Great Pyramid at Gizeh was erected about 2600 B.C. and undoubtedly involved some mathematical and engineering problems. The structure covers thirteen acres and contains over 2.000.000 stone blocks, averaging 2,5 tons in weight. These stones were brought from the other side of the Nile. The Great Pyramid was built by an army of 100.000 slaves working for a period of thirty years, and the sides of the square base involve a relative error of less than 1/14000, and the relative error in the right angles at the corners does not exceed 1/27000