The ancient Egyptians had a unique method of multiplication

The ancient Egyptians had a unique method of multiplication

The ancient Egyptians had a unique method of multiplication that may seem unconventional to us today. Instead of using the standard algorithm we are familiar with, they relied on a doubling method. Despite its apparent simplicity, this method was effective for their calculations. Let's take a closer look at how they performed multiplication.

 

To multiply two numbers, let's say 12 and 13, they followed these steps:

Write down the two numbers	1	12
Double the first number and write it in a separate colum	2	24
Repeat the doubling process	4	48
Continue doubling until the left column exceeds the second number (13 in this case)	8	96
Look at the numbers in the left column that sum up to the second number (13)	1, 4 ,8
Add up the corresponding numbers in the right column		12+48+96=156

 

The result, 156, is the product of 12 and 13.

You can try this method yourself to verify its correctness and gain a sense of the ancient Egyptian approach to multiplication. It's an intriguing way to explore their mathematical techniques and practice your calculation skills. However, once you become familiar with this method, you might wonder why it works.

 

The reason behind the effectiveness of the ancient Egyptian multiplication method lies in the doubling process. By doubling the numbers successively, they were essentially using a binary doubling system. Each doubling step corresponds to a binary digit in the second number. The numbers in the left column represent the binary digits of the second number, and the corresponding numbers in the right column are the products obtained by multiplying the first number by the respective powers of 2.

 

In the case of 12 × 13, the binary representation of 13 is 1101. By selecting the numbers from the left column that correspond to the binary digits (1, 4, and 8) and summing up the corresponding numbers from the right column (12, 48, and 96), we obtain the correct product, 156.

 

This ancient Egyptian multiplication method demonstrates the ingenuity and adaptability of different cultures in developing mathematical techniques suited to their needs and understanding.