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 integers (including negative numbers), rational numbers (fractions) and real numbers is a systematic summary of this basic definition.

Multiplication can also be seen as calculating the objects arranged in a rectangle (integer) or finding the area of a rectangle with a given side length. The area of the rectangle does not depend on which side is measured first, which shows the exchange property. The product of two measured values is a new type of measurement, for example, multiplying the length of two sides of a rectangle to get its area, which is the theme of size analysis.

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Multiplication is one of the simplest operations in arithmetic. It originated from the multiplication of integers.

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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 we use seems simple, but in fact we need to master the formula table of 99 multiplication in advance; Considering this, this vertical calculation is not perfect.

We are about to see what different multiplication methods have been created by different civilizations in the process of mathematical development, and some of them can even completely abandon the multiplication table.

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.

At first, people didn't know what this clay tablet meant. Later, an amazing person found that if these numbers are taken as three decimal places in hexadecimal, then the approximate length of the diagonal of the unit square is exactly:1+24/60+51/602+1603 = 6550.

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, my final paper will have been written. Another archaeological discovery tells us 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.