Multiplication is a shortcut to add up the same numbers. The result of its operation is called product, and "X" is the symbol of multiplication. From the philosophical point of view, multiplication is the result of qualitative change caused by additive quantity. The multiplication of integer, rational number and real number is a systematic summary of this basic definition.

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In the process of arithmetic development of various civilizations, the generation of multiplication operation is a very important step. A civilization can successfully develop counting methods and addition and subtraction operations, but it is not so easy to create simple and feasible multiplication methods.

The vertical calculation of multiplication seems simple, but it is necessary to master the formula table of 99 multiplication in advance; Considering this, this vertical calculation is not perfect. It will soon be seen that in the development of mathematics, different civilizations have created different multiplication methods, and some can even abandon the multiplication table completely.

Ancient Babylonian mathematics used hexadecimal, which was confirmed by a piece of ancient Babylonian clay discovered by archaeology. There is a square on this clay tablet with four numbers 1, 24,51,10 on the diagonal.

When people first discovered this clay tablet, they didn't know what it meant. Later, a cow was surprised to find that if these figures were taken to three of the 60 decimal places, the approximate diagonal length of a unit square would be exactly obtained.

1+24/60+51/602+1603 =1.41421296296 ... This shows that ancient Babylon has mastered the pythagorean system.

The use of hexadecimal has brought great obstacles to the development of multiplication in ancient Babylonian mathematics, because to memorize the multiplication table of 59-59, at least 1000 items must be memorized. By the time you recite it, it is estimated that the final paper has been written. Another archaeological discovery tells how to avoid using multiplication tables in ancient Babylonian mathematics.

Archaeologists have found that some clay tablets are engraved with square tables less than 60, and the value of AB can be obtained by using the formula ab = [(A+B) 2-A 2-B 2]/2.

Another formula is AB = [(a+b) 2-a-b) 2]/4, which shows that the multiplication of two numbers only needs to take the difference between the square of their sum and the square of their difference, and then take half twice. The frequent use of square numbers probably accelerated the discovery of Pythagoras theorem by ancient Babylonians.