The origin of multiplication

The multiplication methods of ancient Greece, ancient Egypt, ancient India and ancient Rome are complicated and inconvenient to remember. Because there is no carry system, in principle, you need an infinite multiplication table, so there is no 99 table. For example, the multiplication table of ancient Greece must list 7x8, 70x8, 700x8, 700x8, 700x8, 700x8, 7000x8…… ... ...

In contrast, since the 99-99 table is based on the decimal system, 7x8=56, 70x8=560, 700x8=5600, 7000x8=56000, and only 7x8=56 is needed for one representation. There was no multiplication table in ancient Egypt. Archaeologists found that the ancient Egyptians calculated the product by repeated addition. For example, to calculate 5x 13, first get 26 from 13+ 13, then add 26+26=52, and then add 13 to get 65.

Ancient Babylonian arithmetic had a carry system, which made great progress compared with Greece and other countries. However, Babylonian arithmetic used a hexadecimal system. In principle, a multiplication table of "59x59" needs 59*60/2= 1770 items; Because the "59x59" multiplication table is too large, the Babylonians never used a "multiplication table" similar to the Jiujiu table.

Archaeologists have never found the multiplication table of "59x59" similar to Jiujiu Table. But archaeologists found that Babylonians used only 1x 1 = 1, 2x2 = 4, 3x3 = 9...7x7 = 49, ... 9x9 = 81...16x/kloc. To calculate the product of two numbers A and B, the Babylonians relied on their best algebra, axb=((a+b)x(a+b)-axa-bxb)/2.