Dyadic Multiplication

 

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For example, to find the product of 13 x 11, in one column they started from 1, doubling in each row until there were enough numbers in that column to add up to the number (in this case 8, 4, and 1 add up to 13); in the corresponding parallel column they started with the second number, and doubled that. They then made an oblique mark against the rows corresponding where the numbers in the first column added up the value of the first number.

Adding only the numbers in the right column where there is a mark (in this case 11 + 44 + 88) gives the final result.

 

13 x 11

1

11

2

22

4

44

8

88

13

143

Division uses the same technique. So to divide 143 by 11, the scribe would build the same table. He would work in the right hand column this time, adding the numbers until he reached 143 and again making marks. Then the answer is the sum of the numbers in the left hand column where the rows have a mark; so 1 + 4 + 8 gives the answer 13. This is fine where there is an exact division, but when fractions are involved, they resorted to a variation on the technique, which is a mixture of multiplication and division.

   

Topics on Egyptian mathematics

Egyptian gods and mathematics

Egyptian numerals

Rhynd and Moscow Papiri

Unit Fractions

Eye of Horus Fractions

Dyadic multiplication

An Egyptian scribe from the Fourth Dynasty. The word scribe is applied to clerks, copyists and, more importantly to the class of bureaucratic officials on whom the whole Egyptian system was based. They were an elite who passed their profession from father to son. Scribes were very powerful, or so we think now, as the popularity of the scribe statues overtakes popularity of any other statues apart from god forms.

To learn about gods which are related to mathematics, or learning, click here.

 

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