THE HISTORY OF MATHEMATICS

• Multiplication in the ancient Egypt:

The knowledge they had was built on that any number was made by adding the part of the selected terms from the binary series (1, 2, , 4, 8 .........)

Ex:

311 times 13

To get 13 we have to divide this number so it only includes number from the binary series. That means 13= 1+4+8

To calculate 311*X we just doubling 311 for each time we doubles the binary parts.

1 311

2 622

4 1244

8 2488

16 4976

When we no are going to calculate 311*13 we just add together the values of each of the binary parts we need to get 15.

1 + 4 + 8 -> 311 + 1244 + 2488 = 4043

• Division in the ancient Egypt:

Multiplication and division are mirror images of one another. Division is the opposite process of multiplication.

Ex.

476 divided by 13

In modern equivalent, you start with the same process as in multiplication.

..... a binary series table .....

1 x 13 = 13

2 x 13 = 26

4 x 13 = 52

8 x 13 = 104

16 x 13 = 208

32 x 13 = 416

Then you take selected parts on the right side and adds: then you get 476.

476 = 416 + 52 + 8 divides them by 13

476 = 416 + 52 + 8

13 13 13

= 32 + 4 + 8 = 36 8

13 13