Account when the ancient Egyptians 2

Account when the ancient Egyptians 2

Beating the ancient Egyptians
Ancient Egyptians devised a way to make the calculation that we know the multiplication process in a way that the use of the combination, and the basic rule followed in the multiplier is numerical . We knew that the ways in which they use them in the account by what we found their tracks in the form of manuscripts such as Papyrus de Moscou and Manuscript Papyrus Rhind. And explain how the successive doubling in the beatings of the following examples :
Example 1 : We want the product 7 . 9 = 63
For result holds beatings , Egyptian writer begins to multiply the number 7 in a row and looking for a result milled (8 + 1 ) , as follows :
> 1 ............. 7
2 .......... 14
4 .......... 28
> 8 .......... 56
16 .......... 112
9 .......... 63
By doubling up at 7 7 . 8 = 56 , and then adds them 7 Faihsal on the result , as the 7 + 56 = 63 .
Example 2 : We want the product 59 . 37 = 2183
Begin to double the number of 59 , respectively , as follows :
* 1 ............. 59
2 .......... 118
* 4 .......... 236
8 .......... 472
16 .......... 944
* 32 .......... 1888
37 .......... 2183
By doubling the 59 we first arrived to the two numbers multiplied by 32 . 59 = 1888 .
Then add it the product ( see the parameter lines ) : ( 4 + 1). 59 = 236 + 59 = 295 , we get the result 2183 .

Divisible by the ancient Egyptians
The division also depends on doubling the numbers respectively Previous explained with beatings, but with some differences to be adapted to meet the purpose .

Ancient Egyptian writer begins to double the number 3 the following steps :
1 .......... 3
2 .......... 6
4 .......... 12
> 8 .......... 24
> 16 ......... 48
32 ......... 96
> 64 .......... 192
88 .......... 264
And the appointment of teacher numbers collected by the index and up to score : 8 + 16 + 64 = 88 .

Example 2:
Past ideals is a simple example , it leads to the quotient of the integer contains no fractures.
In our example, the next lead the process of dividing the 212 ÷ 6 result containing fractions.
We start doubling the number 6 :
> 1 .... 6
> 2 .... 12
4 .... 24
8 .... 48
16 .... 96
> 32 .... 192
> 1 \ 3 .... 2
1 \ 3 +35 .... 212
We have doubled the number 6 until we got to the number 192 , and remained a difference between Nos. 212 and 192 only $ 20 . A review of the first two lines , we find that they fall number 18 and very remains No. 2 in which we find that one - third of the number 6 .
This gets on the outcome of the ancient Egyptian division and the note is as follows : 1 + 2 + 32 + 1 \ 3 = 1 \ 3 35
Example 3:
Egyptian writer was able also using multiplier method dividing the number of small to a large number .

Comparing 4 in relation to the number 7 , we find that the four slightly larger than half the 7 . This we find the first member of the solution, which is 1 /2.
In the next step begins Egyptian old doubling primarily ( 7 ), respectively, as usual :
1 .... 7
* 1 \ 2 .... 1 \ 2 3
1 \ 7 .... 1
* 1 \ 14 .... 1 \ 2
1 \ 1 +14 \ of 2 .... 4
We found the solution : it has come to fully divisor is the number 4 , and combine the two numbers wanted here , we get a solution : 1 \ 14 1 \ 2 .

1 ... 33
1> 2 ... 66
4 ... 132
8 ... 264
2 > 16 ... 528
3 > 32 ... 1056
4> 1 \ 4 ... 1 \ 4 8
5 > 1 \ 33 ... 1
6> 1 \ 44 ... 1 \ 4 1 \ 2
1 \ 44 + 1 \ 33 + 1 \ 4 + 50 ... 1660
And explain the method is as follows : We have doubled the number 33 five times consecutively and we got to number 1056 . We note that the collection of numbers parameter 1056 + 528 + 66 = 1650 . The difference between 1660 and 1650 is 10.
And begin the search for the 33 fractures and found that 10 containing 33 quarter and $ 1 \ 4 8. And became the missing number to supplement the 1660 is 3 \ 4 1 Any one and three quarters. One gives us the number 1 \ 33, and three - quarters are only 1 \ 2 and 1 \ 4 , and three - quarters of the number 1 \ 33 is 1 \ 44 . So we completed 1660 , and result divisible become : 1 \ 44 + 1 \ 33 + 1 \ 4 + 50 .

Rand manuscript
In manuscript Rand ancient Egyptian Rhind explains the expense of space and trigonometry , as we see in this image

Panel offerings
Panel colorful Princess Nfrtiapt of the old state (2565 -2590 BC) tomb at Giza and in front of the numbers of the various offerings. The Louvre, Paris.