Divide a line segment into two parts so that the ratio of one part to the total length is equal to the ratio of the other part to this part. The ratio is [5 (1/2)- 1]/2, and the approximation of the first three digits is 0.6 18. Because the shape designed according to this ratio is very beautiful, it is called golden section, also called Chinese-foreign ratio. This is a very interesting number. We approximate it with 0.6 18, and we can find it by simple calculation:1/0.618 =1.618 (1-0.618). Golden section of line segment (ruler drawing) 1. Let the known line segment be AB, the intersection point B be BC⊥AB, and BC = AB/2; 2. link AC; 3. Make an arc with C as the center, CB as the radius, and AC and D intersect; 4. Make an arc with A as the center and AD as the radius, and intersect AB at P, then point P is the golden section of AB.
How is the golden section 0.6 18 calculated?
How is the golden section 0.6 18 calculated?
The golden section refers to dividing a line segment into two parts so that the ratio of one part to the total length is equal to the ratio of the other part to this part. Its ratio is an irrational number, expressed by a fraction as (√5- 1)/2. The approximation of the first three digits of this irrational number is 0.6 18. Because the shape designed according to this ratio is very beautiful, it is called golden section, also called Chinese-foreign ratio. This demarcation point is called the golden section.
How to calculate the golden section line
Suppose a strong stock rose from 10 yuan to 15 yuan in the last round, showing a strong trend, and then there was a pullback. What price will it be adjusted back to? The 0.382 bit of the golden section is 13.09 yuan, the 0.5 bit is 12.50 yuan, and the 0.61.91yuan, which are the three support positions of the stock. If the stock price is supported around 13.09 yuan, the stock will remain strong. The probability that the market outlook breaks through1the historical high in 5 yuan is greater than 70%-(15-10) * 0.382 =13.0915-(15-/kloc-0). 0.618 =11.91doesn't really count. Stock software has the function of golden section.
The first step in drawing the golden section is to remember some special numbers: 0.191.3820.6180.8091.1.3821. 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 at the golden section line generated by these four figures. Step two, find a point. This point is the highest point at the end of the rising market, or the lowest point at the end of the falling market. Of course, we know that high and low here refer to a certain range and are local. As long as we can confirm that a trend (whether up or down) has ended or temporarily ended, then 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 increase is 10 yuan, then 8.09 =10× 0.809 6.18 =10× 0.618 3.82 =10× 0.388. 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 golden section is the reserve price of this decline multiplied by the special figure above. Suppose the reserve price of this decline is 10 yuan. Then11.91=10×1.12191mutual10× 2. × 2.382 16. 18 =10×/8 26.18 =10× 2.618. In addition, the golden section has another usage. 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. On the watch software, there is a line drawing tool. By selecting "golden back file" or "golden callback" or "vertical golden proportion division", the name of each watch software is different. Then choose a high point and a low point, and you can know the golden ratio relationship between them. 0.6 18 and 0.382 play an especially important role in this relationship. The origin of the golden section: 1. Fibonacci, an Italian mathematician who owns the magic number 13****, discovered this magic number. Namely: 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144 … The sum of the first two numbers is equal to the last one. For example:1+2 = 3; 2+3=5; ..... 55+89 = 144 ... The magic number is even more magical: 1. Compared with the latter figure, the ratio tends to be 0.6 18034 ... (irrational number). Such as:1÷ 2 = 0.5; 2÷3=0.667; 3÷5=0.6; 5÷8=0.625; 8÷ 13=0.6 15; ..... 89 ÷ 144 = 0.6 18 ...2. Compared with the above figure, the ratio tends to 1.6 18. Such as: 5 ÷ 3 =1.667; 8÷5= 1.6; 2 1÷ 13= 1.6 15; 89÷55= 1.6 1 ......
How to calculate the golden section point
The golden ratio is 0.6 18.
Then, suppose there are three points on the line segment, namely A, B and C, then AB = X and BC = Y.
Then x+y = 272 and x ÷ y = 0.6 18.
x = 103.89y = 168 438+00438+0。
So point b is the golden section.
How did the golden section come about?
It is precisely because the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC that modern mathematicians came 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. In his view, the so-called golden section refers to dividing the line segment with length L into two parts, so that the ratio of one part to the whole is equal to the other part. The simplest way to calculate the golden section is to calculate Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 2 1, ... after 2/3, 3/5, 5/8, 8/65438. Around the Renaissance, the golden section was introduced to Europe by * * * people and was welcomed by Europeans. They called it the "golden method", and a mathematician in Europe17th century even called it "the most valuable algorithm among all kinds of algorithms". This algorithm is called "three-rate method" or "three-number rule" in India, which is what we often say now. 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. In fact, the "golden section" is also recorded in China. Although it was not as early as ancient Greece, it was independently created by China ancient algebras and later introduced to India. After textual research. The European proportional algorithm originated in China and was introduced into Europe from India, not directly from ancient Greece. 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 put forward by the American mathematician Kiefer in 1953 and popularized in China in the 1970s.
Edit the introduction of this paragraph.
concept
Divide a line segment into two parts so that the ratio of one part to the total length is equal to the ratio of the other part to this part. The ratio is (√5- 1)/2, and the approximate value of the first three digits is 0.6 18. Because the shape designed according to this ratio is very beautiful and soft, it is called golden section, also called Chinese-foreign ratio. This is a very interesting number. We approximate it with 0.6 18, and we can find it by simple calculation:1.618 ≈1.618 (1-0.618) \
find
Most people think that the origin of the golden ratio comes from Pythagoras. It is said that in ancient Greece, Pythagoras was walking in the street one day. Before he passed the blacksmith's shop, he heard the sound of striking the iron, so he stopped to listen. He found that the blacksmith had a regular rhythm when he was striking iron, and the proportion of this sound was expressed mathematically by Pythagoras. It has been applied in many fields, and later many people devoted themselves to it. Kepler called it "sacred division", and some people called it "golden section". Pythagoras' law appeared only 1000 years after the completion of the pyramid, which shows that it existed very early. I just don't know the answer.
Edit this paragraph to calculate road rates.
brief introduction
The golden wheel algorithm is different from numbers. With regard to the history of development and discovery, modern mathematicians have come to the conclusion that the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC, so the Pythagorean school had contacted 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 put on a mysterious coat, and several Italian pacioli. ......
How to calculate the golden ratio?
Both A and B are positive numbers a:b=b:(a+b) If a= 1, then1:b = b: (1+b) B2 = b+1b 2-b-1=
How to calculate the golden ratio? 20 points
The golden section, also known as Huang Jinlv, means that there is a certain mathematical proportional relationship between the parts of things, that is, the whole is divided into two parts, and the ratio of the larger part to the smaller part is equal to the ratio of the whole to the larger part, and its ratio is 1: 0.6 18 or10/. The above ratio is the ratio that can most arouse people's aesthetic feeling, so it is called the golden section.