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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 
add it to itself, then add the answer to itself and continue:

            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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