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Since the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC, modern mathematicians have come to the conclusion that Pythagoras school had touched and even mastered the golden section at that time.
In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion.
When Euclid wrote The Elements of Geometry around 300 BC, he absorbed eudoxus's research results and further systematically discussed the golden section, which became the earliest treatise on the golden section.
After the Middle Ages, the golden section was cloaked in mystery. Several Italians, pacioli, called the ratio between China and the destination sacred and wrote books on it. German astronomer Kepler called the golden section sacred.
It was not until the19th century that the name golden section gradually became popular. The golden section number has many interesting properties and is widely used by human beings. The most famous example is the golden section method or 0.6 18 method in optimization, which was first proposed by American mathematician Kiefer in 1953 and popularized in China in 1970s.
|..........a...........|
+ - + - + -
| | | .
| | | .
| B | A | b
| | | .
| | | .
| | | .
+ - + - + -
|......b......|..a-b...|
This value is usually expressed in Greek letters.
The wonder of the golden section is that its proportion is the same as its reciprocal. For example, the reciprocal of 1.6 18 is 0.6 18, while1.618 is the same as 1:0.6 18.
The exact value is the root number 5+ 1/2.
Where does the golden ratio come from? Let's look at a string of strange numbers: 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144, 233, 377. ...
(1) The sum of two connected numbers is equal to the number behind them. For example, 1+ 1 = 2, 2+3 = 5, ...
(2) Except for the first two items? Hey? Straight yellow and dark? Thorium? Zhi Tao? The remainder equals a number before the divisor. Such as: 8 ÷ 3 = 2 remainder 2, 13 ÷ 5 = 2 remainder 3.
(3) Except for the first four items, the ratio of each number to its subsequent items is approximately equal to 0.6 18. Such as:13 ÷ 21≈ 0.618,21≈ 34 ≈ 0.618.
(4) Except for the first four items, the ratio of each number to the number mentioned in the preceding paragraph is approximately equal to 1.438+08. Such as:13 ÷ 8 ≈10.6/kloc-0,213 ≈10.6/kloc-8.
(5) Except the first four items, the ratio of each number to the first two items is about 2.6 18, and the ratio of each number to the second item is about 0.382. Such as: 13 ÷ 5 ≈ 2.6 18, 13 ÷ 34 ≈ 0.382.
(6) Multiply 0.6 18 and 1.6 18 in the above (3) and (4) to get the origin of 1. These numbers are also called mysterious numbers, and 0.6 18 and 0.382 are called the golden ratio.
In addition, the above singular combination not only reflects the two basic proportions of the golden section of 0.6 18 and 0.382, but also has the following two mysterious proportions, namely:
( 1)0. 19 1,0.382,0.5,0.6 18,0.809
(2) 1, 1.382, 1.5, 1.6 18,2,2.382,2.6 18……
As a technical index, the golden ratio is used in stock price prediction as follows: We take the important peak or bottom of the recent stock price trend, that is, the important high or low point, as the basis for estimating the trend. When the stock price rises, we take the bottom stock price as the base, and when its increase is close to the golden ratio, such as 0.382 or 0.6 18, it is easy to encounter resistance; When the stock price falls, based on the peak stock price, its decline is easier to be supported when it reaches a certain golden ratio. When the market draws to a close, the stock price rises or falls sharply, and its rise and fall reaches an important golden ratio, the situation may turn for the better. When the market turns, whether it stops falling or rising, the difference between the recent peak and trough in the recent trend is taken as the measuring base, and the original price is divided into five gold points according to 0. 19 1, 0.382, 0.5, 0.6 18, 0.809, and the stock price is reversed.
Because the golden ratio contains some special meanings that are not based on system theory, it is somewhat mysterious. Some people think that it is purely coincidental and should not be kept secret. However, a large number of facts show that the golden ratio conforms to certain statistical laws. The golden ratio has also been applied by Eliot's wave theory, becoming a world-famous wave theory model and widely adopted by investors.