Egyptian Method of MultiplicationDate: 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/ |
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