The origin of golden ratio
The golden ratio, named Phi in English, is named after the Greek sculptor phidias. It means that the ratio of small parts to most parts after image segmentation is equal to the ratio of most parts to total parts (equal to 1: 1.6 18), and this segmentation ratio is considered to be the most beautiful. A quadrilateral that meets this ratio is called a golden rectangle and is considered to be the most pleasing quadrilateral.
What is the golden ratio?
The golden ratio, also known as the golden ratio, divides 1 into 0.6 18 and 0.382, and then evolves other calculation methods according to the actual situation. When the rising rate approaches or reaches 0.382 and 0.6 18, the rising rate will change, in other words, when the rising rate approaches or exceeds 38.2% and 6 1.8%, there will be pressure.
Derivation of gold cutting rate
In addition to the two inherent back pressure points of 0.382 and 0.6 18, 0. 19 1 is also an important point, which is half of 0.382. In other words, when the rising market unfolds, we must first predict the ability of the stock price to rise and the possible reversal position. One method is to multiply the lowest point of the last downward trend by 0. 19 1, 0.382, 0.6 18, 0.809, 1, and when the increase is more than doubled, the back pressure is1./kloc-0.
The golden ratio of nature
Many biological forms conform to the golden ratio, for example, each finger has three knuckles, that is, one from the base to the next? About six times. From shells to petals to buildings, the golden ratio is everywhere. The five-pointed star is the symbol of Pythagoras school, and its length and length are in line with the golden ratio in turn. The golden ratio is also reflected in wonderful poetic music, including Bach's refrain of fugue in D minor and Goya by Russian poet Woznetsky.
.
.
.
.
.
The teaching dialogue about the golden section in dan brown's The Da Vinci Code can make you know more about the golden section:
They came to the emergency staircase entrance, and Sophie opened the door carefully. There is no alarm, only the door outside the Louvre is connected to the alarm network. Sophie led Langdon down the zigzag stairs to the first floor. They stepped up their pace.
Langdon quickly followed Sophie's footsteps and asked, "When your grandfather talked about the five-pointed star, did he mention goddess worship or resentment against the Catholic Church?"
Sophie shook her head. "I prefer to analyze it from a mathematical point of view-golden section, PHI, Fibonacci sequence and so on."
Langdon was surprised. "Did your grandfather teach you PHI?"
"Of course, the golden section." She said shyly, "Actually, he joked that I was half in line with the golden section … that's because of the spelling of my name."
Langdon thought for a moment and muttered, "So-phi-e."
When Langdon came downstairs, he thought of PHI again. He began to realize that the clues left by Sauniere were more complete than he had imagined.
Leonardo da vinci ... Fibonacci sequence ... pentagram.
Incredibly, all these are linked by a concept in art history, and Langdon often spends hours explaining this very basic concept. The 2nd1letter in Greek
He suddenly had an illusion, as if he had returned to Harvard, stood on the platform of the classroom and explained Symbols in Art, and wrote down his favorite number on the blackboard: 1.438+08.
Langdon turned to the eager students in the audience and asked, "Who can tell me what this number is?"
A big math student sitting in the back raised his hand and said, "That's PHI." He pronounced it "no"
"Well said, Stiehler." Langdon said, "Everyone knows PHI."
Stiehler added with a smile, "Don't confuse it with PI(π). We mathematicians like to say: PHI has one more H, but it is much better than PI! "
Langdon smiled, but the others didn't understand.
Stiehler sat down with a bang.
Langdon continued: "PHI, 1.438+08 plays an extremely important role in art. Who can tell me why?"
"Because it's beautiful?" Stiehler tried to save his face.
Everyone burst into laughter.
"Actually, Stiehler was right again," Langdon said. PHI is usually considered to be the most beautiful number in the world. "
The laughter suddenly stopped. Stiehler is complacent.
Langdon put a picture on the slide projector, explaining that PHI originated from Fibonacci sequence-this sequence is very famous, not only because the sum of two adjacent terms in the sequence is equal to the latter term, but also because the quotient obtained by dividing two adjacent terms is about 1.6 18, which is PHI.
Langdon went on to explain that from a mathematical point of view, the origin of PHI is quite mysterious, but what is even more puzzling is that it also plays an extremely important role in the composition of nature. Plants, animals and even humans all have characteristics strikingly similar to this ratio.
Langdon turned off the lights in the classroom and said, "It is obviously no coincidence that PHI is everywhere in nature, so our ancestors estimated that PHI was set by the creator in advance. Early scientists called 1.6 18 the golden section. "
"Wait a minute," said a girl sitting in the front row. "I am a biology major. I have never seen the golden section of nature. "
"no?" Langdon grinned. "Have you studied the males and females in the hive?" "Of course. There are always more women than men. "
"yes. Do you know that?/You know what? Do you know that?/You know what? If you separate males from females in any hive in the world, you will get the same proportion. "
"Really?"
"Yes, it is PHI."
The girl was dumbfounded. "This is impossible."
"Maybe!" Langdon countered. He smiled and released a slide of spiral shells. "Know this?"
"Nautilus," the student replied. "A mollusk that adjusts its buoyancy by inhaling air from its shell."
"That's right. Can you guess the ratio of the diameter of each rib to the diameter of the adjacent ribs? "
The girl looked at the concentric arc on the spiral nautilus and couldn't say the exact answer. Langdon nodded and said, "PHI. Golden section. 1.6 18。 "
The girl showed a surprised expression.
Langdon then released the next slide-a close-up of sunflower. Sunflower seeds are arranged in opposite arcs on the disk. Can you guess the diameter ratio between two adjacent turns? "
“PHI？” Some people say.
"That's right." Langdon began to play slides quickly-spiral pinecones, the arrangement of leaves on plant stems, and the division of insects-all of which were completely in line with the golden section.
"It's incredible!" Someone shouted.
"Yes, but what does this have to do with art?" Another person said.
"ah! Good question. " Langdon said, and released another slide-Leonardo da Vinci's famous male nude painting "Vitruvian Man". This picture is on a piece of parchment, which has been slightly yellowed. The name of this painting is named after the outstanding Roman architect Mark Vitruvi, who praised the golden section in his book Architecture.
"No one knows the subtle structure of the human body better than Peter Finch. In fact, Leonardo da Vinci once excavated the human body to measure the exact proportion of the human skeleton structure. He was the first person to claim that the proportion of human body structure is completely in line with the golden ratio. "
Everyone present gave Langdon a suspicious look.
"Don't believe it?" "Next time you take a shower, take a tape measure," Langdon said. Several students from the football team snickered.
"It's not just you athletes who become restless," Langdon suggested. "All of you, boys and girls, have a try. Measure your height and divide it by the distance from your navel to the ground. Guess what the result is. "
"It can't be PHI!" A sports student said in a skeptical tone.
"it's PHI," Langdon replied. "Yes 1.6 18. Want to see another example? Measure the distance from shoulder to fingertip, and then divide it by the distance from elbow to fingertip to get PHI. PHI can be obtained by dividing the distance from hips to the ground by the distance from knees to the ground. PHI can be obtained from the sections of finger joints, toes and spine. Friends, each of us is a creature that cannot live without the golden section. " Although all the lights in the classroom were turned off, Langdon could see that everyone was shocked. A warm current surged into his mind, which is why he loves teaching. "My friends, as you can see, complex nature hides rules. When the ancients discovered PHI, they must have accidentally discovered the scale of God's creation, and because of this, they were full of admiration for nature. God's masterpiece can be found in nature, and there is a pagan organization-Mother Earth. Many of us praise nature like pagans, but we don't realize it ourselves. For example, our celebration of May Day is a good example. Mayday is a festival to celebrate spring. Through this festival, people celebrate the recovery of the earth and give gifts to mankind. From the beginning, the mysterious nature of the golden section has been determined. People can only act according to the laws of nature, and art is an attempt to imitate the beauty created by the creator, so we will see many examples of the golden section in works of art this semester. "
In the next half hour, Langdon showed the students slides of works by Michelangelo, Albrecht Dürer, Leonardo da Vinci and many other artists, who consciously followed the golden ratio when designing and creating their works. Langdon revealed the golden ratio used in the architectural design of the Parthenon, the Egyptian pyramids and even the United Nations building in new york, and pointed out that PHI was also used in Mozart's sonata, Beethoven's Fifth Symphony and the creation of musicians such as Bartok, Debussy and Schubert. Langdon also told everyone that even when stradivari made his famous violin, he used the golden section method to determine the exact location of the F-shaped hole.
Langdon went to the blackboard and said, "Let's go back to symbols." He drew a five-pointed star composed of five straight lines on the blackboard. "This is the most symbolic figure you will learn this semester. The five-pointed star-called the five-pointed star by the ancients-is considered sacred and magical in many cultures. Who can tell me why? "
Stiehler, a math major, raised his hand again. "Because if you draw a five-pointed star, those line segments will automatically cut themselves into several segments according to the golden ratio."
Langdon nodded to the young man and was proud of him. "Good answer. The proportion of line segments in the five-pointed star conforms to the golden section rate and is the primary representative of the golden section. It is for this reason that the five-pointed star is always regarded as a symbol of beauty and perfection, and is associated with goddesses and sacred women. "
All the girls in the class are smiling.
This is an ancient mathematical method. Its magical functions and magic power have not been clearly explained in mathematics so far, but in practice it is found that it often plays an unexpected role.
Here is to explain how to get the golden section line, and according to the golden section line to guide the next operation of buying and selling stocks.
There are two kinds of golden section: one-point golden section and two-point golden section.
Here's the method: there are two factors in drawing a single point (one is the golden number, the other is the highest point or the lowest point)
The first step in drawing the golden section is to remember some special numbers:
0. 19 1 0.382 0.6 18 0.809
1. 19 1 1.382 1.6 18 1.809
2. 19 1 2.382 2.6 18 2.809
Among these figures, 0.382, 0.6 18, 1.382, 1.6 18 are the most important, and the stock price is likely to generate support and pressure at the golden section generated by these four figures.
Step two, find a point. This point is the highest point when the rising market turns around, or the lowest point when the falling market turns around. Of course, we know that the high and low points here refer to a certain range and are local. As long as we can confirm that a trend (whether up or down) has been tied up or temporarily ended, the turning point of this trend can be used as the golden section point. Once this point is selected, we can draw the golden section line.
When the rising market begins to reverse, we are extremely concerned about where this decline will be supported. The golden section provides the following price points. They are multiplied by several special figures listed above, and then multiplied by the peak price of this rise. Assuming that the peak of this rise is 10 yuan, then
8.09= 10×0.809
6. 18= 10×0.6 18
3.82= 10×0.382
1.9 1= 10×0. 19 1
These prices are very likely to be the support, among which 6. 18 and 3.82 are the most likely.
In the same way, when the falling market starts to turn around, we are concerned about where the rising market will be under pressure. The position provided by the gold thread is the reserve price of this decline multiplied by the special figure above. Assuming that the price of Luogu is 10 yuan, then
1 1.9 1= 10× 1. 19 1 2 1.9 1= 10×2. 19 1
13.82= 10× 1.382 23.82= 10×2.382
16. 18= 10× 1.6 18 26. 18= 10×2.6 18
18.09= 10× 1.809 28.09= 10×2.809
20= 10×2
It is likely to become the pressure level in the future. Among them, 13.82 and 16. 18 and 20 yuan are the easiest pressure lines, and those exceeding 20 are rarely used.
In addition, there is another usage of the golden section, that is, the two-point golden section.
Select the highest point and lowest point (local), take this interval as the whole length, and then make the golden section line on this basis to calculate the rebound height and reverberation height. This golden section line is actually a special case of percentage line.