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Egyptian Method of Multiplication

Date: 6/26/96 at 19:4:52
From: Carrie Shelley
Subject: Egyptian Method of Multiplication

Hi!

Have you ever heard of an Egyptian Method of Multiplication?

Thank you,
Carrie

Date: 6/26/96 at 20:15:34
From: Doctor Jodi
Subject: Re: Egyptian Method of Multiplication

Hi Carrie! Yes, we have.... Here's a description of the method, from

http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Babylonian_and_Egyptian.html

Unlike the Greeks, who thought abstractly about mathematical ideas,
the Egyptians were only concerned with practical arithmetic. In fact
the Egyptians probably did not think of numbers as abstract quantities
but always thought of a specific collection of 8 objects when 8 was
mentioned. To overcome the deficiencies of their system of numerals
the Egyptians devised cunning ways around the fact that their numbers
were unsuitable for multiplication, as is shown in the Rhind papyrus
which date from about 1700 BC.

The Rhind papyrus recommends that multiplication be done in the
following way. Assume that we want to multiply 41 by 59. Take 59 and

41          59
______________
1          59
2         118
4         236
8         472
16         944
32        1888
______________

Since 64 > 41, there is no need to go beyond the 32 entry. Now go
through a number of subtractions

41 - 32 = 9, 9 - 8 = 1, 1 - 1 = 0

to see that 41 = 32 + 8 + 1. Next check the numbers in the righthand
column corresponding to 32, 8, 1 and add them.

59
______________
1          59     X
2         118
4         236
8         472     X
16         944
32        1888     X
______________
2419

Notice that the multiplication is achieved with only additions; notice
also that this is a very early use of binary arithmetic. Reversing the
factors we have

59          41
______________
1           41     X
2           82     X
4           16
8          328     X
16          656     X
32         1312     X
_______________
2419

Enjoy!  Let us know if you need more help.

-Doctor Jodi,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

Associated Topics:
Elementary Math History/Biography
Middle School History/Biography

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