1/0.6 18= 1.6 18
( 1-0.6 18)/0.6 18=0.6 18
Let's talk about a series. The first few digits are: 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144 ... The characteristic is that every number is the sum of the first two numbers except the first two numbers (the numerical value is 1).
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.
This Fibonacci number not only starts from 1, 1, 2, 3, 5 ... Like this, if you choose two integers at will and sort by Fibonacci number, the ratio between the two numbers will gradually approach 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, a regular pentagram and a regular pentagon can be made.
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 to the whole is equal to the ratio of the other 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. Golden ratio and golden rectangle can bring beauty to the picture, which can be found in many works of art and nature. The Pasa Shennong Temple in Athens, Greece is a good example. Leonardo da Vinci's is in line with the golden rectangle. The face also conforms to the golden rectangle, and the proportional layout is also applicable.