Introduction to multiplication:
1, multiplication, refers to the shortcut of adding 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.
2. Multiplication can also be regarded 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.
3. "99 Multiplication Song" is also often called "Little 99". The formula for students to learn "elementary ninety-nine" is from "11" to "998 1", while in ancient times, it was the other way around, from "998 1" to "224".
Because the first two words of the formula are "99", people call it "99" for short. It was only in the 13 and 14 centuries that "one person gets a ... 998 1" was reversed.
5. China used the "99 formula" earlier. Sentences such as "3927", "684 18", "483 12" and "6636" can be found in books such as Xunzi, Guanzi, Huainanzi and Warring States Policy. It can be seen that as early as the Spring and Autumn Period and the Warring States Period, 99 multiplication songs became popular.
Expand knowledge:
1. 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.
3. 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 found this clay tablet, they didn't know what it meant. Later, an amazing person found that if these figures were taken as three decimal places in hexadecimal, they would get exactly the approximate length of the diagonal of the unit square:1+24/60+51/602+1603.
5. 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.
6. Archaeologists found that some clay tablets were engraved with Fiona Fang's 60-mile square table. Using the formula ab = [(A+B) 2-A 2-B 2]/2, the value of ab can be quickly obtained. 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.
7. The frequent use of square numbers probably accelerated the discovery of Pythagoras theorem by ancient Babylonians.