Egyptian Method of MultiplicationDa

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/

ผลลัพธ์ (อังกฤษ) 1:

Egyptian Method of MultiplicationDate: 6/26/96 at 19:4:52From: Carrie ShelleySubject: Egyptian Method of MultiplicationHi!Have you ever heard of an Egyptian Method of Multiplication? Thank you,CarrieDate: 6/26/96 at 20:15:34From: Doctor JodiSubject: Re: Egyptian Method of MultiplicationHi 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, 9-1, 1-8 = 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 ______________ 2419Notice 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 _______________ 2419Enjoy! Let us know if you need more help.-Doctor Jodi, The Math Forum Check out our web site! http://mathforum.org/dr.math/

ผลลัพธ์ (อังกฤษ) 2:

Egyptian Method of Multiplication Date: 06/26/96 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 8:15:34 p.m. 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, abstractly About Who thought. 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 Objects Collection of 8 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. Want to assume that we Multiply 41 by 59. Take 59 and Add it to Itself, then the answer to Itself and Continue Add: 41 59 ______________ 1 59 2 118 4 236 8 472 16 944 32 1888th ______________ Since 64> 41, there is. no need to go beyond the 32 entry. Go now Number of subtractions Through a 41 - 32 = 9, 9 - 8 = 1, 1 - 1 = 0 to + 8 + 32 = 41 See that 1. Check the Next Numbers in the righthand column corresponding to 32, 8, 1. and Add them. 59 ______________ 1 X 59 2 118 4 236 8 472 X 16 944 X 32 one thousand eight hundred and eighty-eight ______________ 2 419 Notice that the Multiplication is achieved only with Additions; Notice also that this is a very Early use of binary arithmetic. Reversing the factors we have 59 41 ______________ 1 X 41 X 2 82 4 16 8 328 X 656 X 16 X 32 1,312th _______________ 2419 Enjoy! Let US know if You Need Help more. -Doctor Jodi, The Math Forum Check out our Web Site! http://mathforum.org/dr.math/

ผลลัพธ์ (อังกฤษ) 3:

Egyptian Method of Multiplication


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

!

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 itselfThen 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.