Most people think that the origin of the golden section 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 in striking iron, and the contrast 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 did not appear until 1000 years after the completion of the pyramid, so it has existed for a long time. I just don't know the answer. 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 radical sign whose ratio is 5/2- 1/2 or half minus one, and the approximate value 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 use 0.6 18 to approximate it, and we can find it by simple calculation:

1/0.6 18= 1.6 18

( 1-0.6 18)/0.6 18=0.6 18

This kind of value is not only reflected in painting, sculpture, music, architecture and other artistic fields, but also plays an important role in management and engineering design.

One way to make the golden section point is to start with a series. The first digits of the series are: 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 1 49.

What is the relationship between Fibonacci sequence and golden section? It is found that the ratio of two adjacent Fibonacci numbers gradually tends to the golden section ratio with the increase of the series. That is f (n)/f (n-1)-→ 0.618. Because Fibonacci numbers are all integers, and the quotient of the division of two integers is rational, it is just approaching the irrational number of the golden ratio. But when we continue to calculate the larger Fibonacci number, we will find that the ratio of two adjacent numbers is really very close to the golden ratio.

A telling example is the five-pointed star/regular pentagon. The pentagram is very beautiful. There are five stars on our national flag, and many countries also use five-pointed stars on their national flags. Why? Because the length relationship of all the line segments that can be found in the five-pointed star conforms to the golden section ratio. All triangles that appear after the diagonal of a regular pentagon is full are golden section triangles.

The golden triangle has another particularity. All triangles can generate triangles similar to themselves with four congruent triangles, but the golden section triangle is the only triangle that can generate triangles similar to itself with five congruent triangles instead of four congruent triangles.

Because the vertex angle of the five-pointed star is 36 degrees, it can also be concluded that the golden section value is 2Sin 18.

The golden section is approximately equal to 0.6 18: 1.

Refers to the point where a line segment is divided into two parts, so that the ratio of the length of the original line segment to the longer part is the golden section. There are two such points on the line segment.

Using two golden points on the line segment, we can make a regular pentagram, a regular pentagon and so on.

More than 2000 years ago, Odox Sass, the third largest mathematician of Athens School in ancient Greece, first proposed the golden section. The so-called golden section refers to dividing a line segment with length L into two parts, so that the ratio of one part (long part) to the whole is equal to the other part (short part). The simplest way to calculate the golden section is to calculate the ratio of the last two numbers of Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 2 1, ... 2/3, 3/5, 5/8, 8/655.

Around the Renaissance, the golden section was introduced to Europe by Arabs 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.

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. European proportional algorithm originated in China, and was introduced to Europe from Arabia via India, not directly from ancient Greece.

Because it has aesthetic value in plastic arts, it can arouse people's aesthetic feeling in the design of length and width of arts and crafts and daily necessities, and it is also widely used in real life. The proportion of some line segments in the building adopts the golden section scientifically. The announcer on the stage is not standing in the center of the stage, but standing on the side of the stage. The position at the golden section of the stage length is the most beautiful and the sound transmission is the best. Even in the plant kingdom, the golden section is used. If you look down from the top of a twig, you will see that the leaves are arranged according to the golden section law. In many scientific experiments, a method of 0.6 18 is often used to select the scheme, that is, the optimization method, which enables us to arrange fewer experiments reasonably and find reasonable western and suitable technological conditions. It is precisely because of its extensive and important application in architecture, literature and art, industrial and agricultural production and scientific experiments that people call it the golden section.

The golden section is a mathematical proportional relationship. The golden section is strict in proportion, harmonious in art and rich in aesthetic value. Generally, it is 0.6 18 in application, just as pi is 3. 14 in application.

The aspect ratio of a golden rectangle is the golden ratio. In other words, the long side of a rectangle is 1.6 18 times of the short side. The golden ratio and the golden rectangle can bring aesthetic feeling to the picture, which is pleasant. It can be found in many artistic and natural works. The Parthenon in Athens, Greece is a good example. Leonardo da Vinci's Vitruvian Man fits the golden rectangle. Mona Lisa's face also conforms to the golden rectangle, and The Last Supper also applies this proportional layout. Give you a link/view/18 16.htm? fr=ala0