African Origin of Mathematics

Rhind Papyrus

The 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 is greater than 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 right hand 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
 

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