Is the golden ratio really ubiquitous in life?

Yes, not only architecture, but also economics.

Segmentation first appeared in ancient Greece, or was proposed by the Greek mathematician and philosopher Pythagoras 2500 years ago: if the ratio of one part of a line segment to the other part is exactly equal to the two parts, then the sum of the whole line segments of dividing the line segment into two parts can be calculated as. About 200 years later, the mathematician Euclid wrote this definition in the Geometry Primitives:

The line segment is divided into two segments. When the ratio of the long line segment to the ** segment is equal to the ratio of the entire line length to the long line segment, the ratio is ** split. Its ratio is:

By calculating, we find that the number can never be divided, it is an infinite non-repeating decimals. Even so, it did not affect people for a long time, seeing it as the first law of aesthetics and applying it completely to the fields of architecture, art, design, etc., which gave the festival a great reputation.

The first person to be attracted to the proportions was probably the architect. The rules that ancient Greek architects followed when building doors, windows, and even entire buildings. The Parthenon and the Pyramids of Giza strictly follow this aesthetic principle.

Modern society has expanded the scope of its application. Books, newspapers, postcards, billboards, and greeting cards are engraved with a ** dividing mark on the aspect ratio, which is completely copied or deliberately approached to that ratio. If you use an Apple phone, you can take a closer look at the logo on the back.

Its design is a testament to the magic of segmentation.

You'd never think that even in an economy where you can't play eight tricks, this magical ratio has its own unique charm. We know that the higher the product, the better, or the lower, the better.

How to set a ** that can make you profitable and attract consumers to the greatest extent is indeed a great science.

For example, the cost price of your water bottle is 5 yuan. In order to avoid losses, the minimum profit you can accept is 20, that is, the minimum ** of the water cup is 6 yuan, and the most ** of the same kind of water cup on the market is 12 yuan. **=6(12-6) RMB.

Knowledge points: A line segment is divided into two sections, when the ratio of the first segment to the long line segment is equal to the ratio of the long line segment to the length of the whole line, the ratio is ** division, and its ratio is.

Those who have read "The Three-Body Problem" are certainly no strangers to Wei Cheng, a genius mathematician who studied the mathematical model of three-body movement. This lazy guy has some superhuman talents, such as if you draw a line, he **draws a line, and the position must be at the **dividing place.

**The first segmentation appeared in people's field of vision, or 2500 years ago, the Greek mathematician and philosopher Pythagoras proposed: divide a line segment into two parts, if the ratio of one part to the other part is exactly equal to the ratio of one of the two parts to the whole line segment, the ratio can be calculated. About 200 years later, the mathematician Euclid wrote this definition in the Geometry Primitives:

A line segment is divided into two segments, when the ratio of the long line segment to the ** segment is equal to the ratio of the whole line length to the long line segment, the ratio is ** division, and its ratio is. Through calculation, we will find that this number is never divisible and is an infinite non-cyclic decimal number. Despite this, it has not been able to influence people who have long regarded it as the golden rule of aesthetics, and fully applied it to architecture, art, design and other fields, so that the division has won a huge reputation.

The first to be fascinated by the ** segmentation ratio is likely to be the architect. Architects in ancient Greece followed the rules of length-to-width ratios when building doors, windows, and even entire buildings. The Parthenon and the Pyramids of Giza strictly follow this aesthetic rule.

Modern society has expanded its application, books, newspapers, postcards, billboards, greeting cards, etc., the ratio of length and width, etc., are imprinted with the traces of the first division rate, completely copied or deliberately close to the ratio. If you are using an Apple phone, you can take a closer look at the logo on the back, its design proves the magic of the splitting ratio.

You wouldn't expect that even in the realm of an economy where eight strokes can't be beaten, this magic ratio number has its own unique charm. We know that the highest quality of the product is not the higher the better, nor the lower the better, how to set a profit that can not only make its own profits, but also attract consumers to the greatest extent, is really a great knowledge. Are there shortcuts?

Of course, it's for the help of ** split ratio.

Product ** = lowest + (most **grid - lowest**).

For example, the cost of the water cup you sell is 5 yuan, in order to avoid losses, the minimum profit you can accept is 20%, that is, the minimum ** of the water cup is 6 yuan, and the most ** price of the same kind of water cup in the market is 12 yuan, then the ** of the water cup = 6 + (12-6) yuan.

The relationship between our human body and the ** segmentation rate, not to mention. Standard beauty Audrey Hepburn, the ratio of her cheek width to length, the ratio of nose width to nose length, and the ratio of body length above the navel to the length below ......Everything!

Now you should always believe that the ** segmentation rate is really everywhere in life!

That's right, the split ratio is very widely used, so it is ubiquitous in life.

I don't think so, this kind of thing still has to be analyzed according to a specific one.

This should be, after all, there are a lot of ** divisions in life.

Examples of splits in life are:

1. Sunflower flower plate.

The sunflower flower disc is made up of curves intertwined clockwise and counterclockwise. The ratio of the clockwise curve to the counterclockwise curve is the ratio of the split.

2. The length of the butterfly and the length of the wings are approximately divided.

3. There is also the world-famous painting "Mona Lisa", which is composed according to the proportion of ** division.

4. There is also ** division in the regular pentagon.

5. Nautilus, in fact, according to the Fibonacci sequence, take the squares with side lengths respectively, and then draw a quarter of the curve with a vertex of each square as the center of the circle, and then connect all the curves, and the final spiral formed is the ** spiral.

History of segmentation.

In ancient Greece, Pythagoras was walking down the street one day, and before passing by a blacksmith's shop, he heard a very nice sound of a blacksmith striking iron, so he stopped to listen. He found that the blacksmith had a regular rhythm of ironing, and the proportions of this sound were mathematically expressed by Pythagoras.

In the 6th century B.C., the Pythagoreans of ancient Greece studied the drawing of regular pentagons and regular decagons, and most of the origins of the division ratio are believed to come from the Pythagorean school. 1: It is ** division. It was a great find.

1. Applied to photography, the photographic works taken with the best proportion are more in line with the physiological structure of the human eye, making it easier for people to discover its beauty. 2. Applied to human body sculpture, the famous statues of ancient Greece, Venus with broken arms and Apollo, the sun god, were extended to their legs when designing, so that the ratio to their height was applied to painting, in Leonardo da Vinci.

The Vitruvian Man

Mona Lisa and The Last Supper

** division is used.

4. Applied to books, the best proportion of books, newspapers, magazines make people more comfortable to read.

5. Applied to displays, 16:9 displays are becoming more and more popular, which is also related to the first ratio of reading. The business cards printed by people are also in proportion.

6. Applied to the stage, the host of the program will never stand on the stage, but always stand at 1 3 places on the stage, and the position near the top of the stage is the best position.

**Partition has strict proportionality, artistic arguity, harmony, and contains rich aesthetic value, this ratio can arouse people's sense of beauty, and is considered the most ideal proportion in architecture and art.

**The application and examples of segmentation in life are as follows:

1. The ratio of their legs to their bodies is also similar to that of the fashion models with beautiful postures and slender bodies and the dancers who are dancing.

2., the paper used in life is the first rectangle, such a rectangle makes people look comfortable and pleasing to the eye, the paper obtained by the formal cutting method, regardless of its size, such as for, 8 open, 16 open, 32 open, etc., are still approximate **rectangle.

3. The host of the program will never stand on the stage, but always stand at 1 3 places on the stage, and the best position is to stand near the top of the stage.

4. The Italian painter Leonardo da Vinci, who studied human anatomy very much, discovered that the navel of the human body is located at the length of the body. Scientists have also found that people feel most comfortable when the outside ambient temperature is times the temperature of the human body.

5. Whether it is the pyramids of ancient Egypt, or the Notre Dame Cathedral in Paris, or the Eiffel Tower in France in recent centuries, there are relevant data. Also, in the design of ancient Greek temples, ** division was used. People also found that the themes of some famous paintings, sculptures, and photographic works are mostly in the middle of the picture.

Artists believe that the horse of a stringed instrument is placed at the place of the strings, which makes the sound softer and sweeter.

Example 1 The aspect ratio design of the national flag, the best ratio to be strictly observed.

Example 2 If you look closely at the center of a sunflower, you will see that there seems to be a spiral curve in the center. This is calculated to give the best split ratio.

Example 3 The construction of the Parthenon in ancient times also has traces of the division ratio to a certain extent.

Example 4 To get the best timbre of the erhu, its "thousand catties" must be placed at the length of the strings.

Example 5 The design of many web pages refers to the ** division ratio, and the layout of the layout as a whole gives people a sense of breathing, orderly, and hierarchical visual experience, which makes the layout of the web page more pleasing to the eye.