Who came up with the golden ratio? What is the golden ratio?

The mathematician Fabrens wrote a book in the 13th century about the combination of some singular numbers. The combination of these singular numbers is that any one number is the sum of the first two numbers, 5 3, and so on. Some say that these figures were derived from his research pyramids.

The pyramid is closely related to the singular numbers listed above. The geometry of the pyramid has five faces, eight sides, and a total of thirteen levels. When you look at it from either side, you can see three levels.

The length of the pyramid is 5,813 inches (5-8-13), and the percentage ratio of the high base and bottom is 0 618, which is any two consecutive ratios of the above mysterious numbers, such as 55 89 0 618, 89 144 0 618, 144 233 0 618.

In addition, the length of any side of a pyramidal pentagonal tower is equal to 0 618 of the diagonal diagonal. Also, the total number of the bottom four sides is 36524 22 inches, a number equal to a hundred times the light year!

It's an interesting set of numbers. The reciprocal of 0 618 is 1 618. For example, 144 1 168 and 0 618 0 5 168 equals 1.

Another person has studied sunflowers and found that sunflower flowers have 89 braids, 55 facing one side and 34 facing the other. Mysterious? Yes, this set of numbers is called mystery numbers.

And 0 618 and 1 618 are called golden sections.

** Segmentation with human beauty.

In the study, it was found that in the appearance structure of bodybuilders, many data are related to "** segmentation". The human body segmentation factors include 18 "** points", such as the umbilicus is the division point from the top of the head to the sole of the feet, the Adam's apple is the division point from the top of the head to the umbilicus, and the interglabellar point is the division point from the origin point to the chin. 15 "rectangles", such as torso contour, head contour, facial contour, lip contour, etc.; 6 "** indexes", such as the nasolabial index refers to the ratio of the width of the nasal wing to the length of the mouth cleft, the lip index refers to the ratio of the length of the mouth cleft to the distance between the two eyes, and the lip height index refers to the ratio of the height of the upper and lower lip redness on the midline of the face. 3 "** triangles", such as the triangle on the front of the outer nose, the triangle composed of the root point of the nose to the corner points of the mouth on both sides, etc.

In addition, in recent years, domestic scholars have successively found that the relevant "** segmentation" data, such as the ratio of length to width of the anterior teeth, the ratio of eyebrow spacing to the medial canthal spacing, etc., are close to the proportional relationship of "** segmentation".

Proportionality Proportion is an irrational number defined as (1+ 5) 2.

It is used in a wide range of fields: mathematics, physics, architecture, and fine arts. As well as the human body.

The unique properties of proportions are first applied to splitting a straight line. If the total length of a straight line is the denominator plus the unit length of the numerator in the proportion, if we divide it into two halves, the longer is the numerator unit length, and the short one is the mother-child unit length, then the ratio of the length of the long line to the length of the ** is the ratio.

Proportionsis defined as (5-1) 2Irrational numbers。It is used in a wide range of levels, such as: mathematics, physics, architecture, art and even **.

The unique properties of proportions are first applied to splitting a line segment.

If there is a segment whose total length is the denominator of the ratio.

Add the unit length of the numerator, if we divide it into two halves, the long is the length of the denominator unit, and the short one is the length of the numerator, then the ratio of the length to the length of the long line is the proportion. **Ratio approximately: 1.

Split ratioApplication in life:

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 Venus with broken arms in ancient Greece and Apollo, the god of the sun, were extended to their legs when designed, so that the ratio of their height to the height was applied to painting, in Leonardo da Vinci's work "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 monitors are becoming more and more popular, which is also related to the first ratio of reading. The business cards that people print 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.

**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.

The proportion of Huang Yan Gao Jin is rough and auspicious: (5-1).

**The rectangular Iwate is characterized by: length and width = width length - width).

**Ratio is a special mathematical ratio, usually we will use line segmentation to explain this ratio: a line segment is divided into two parts, the ratio of the length of the shorter part to the longer part is equal to the ratio of the length of the longer part to the overall length, and the ratio is an irrational number, and the approximate value of the first three digits is. When applied to a design piece, this proportion creates an artistic feel.

It is recognized by the public as the most aesthetically significant proportion number, and it is also the proportion that can arouse people's aesthetic sense. The proportion and division in product design are also very particular, and are generally determined in the three views of the design. In addition to satisfying aesthetics and ensuring functionality, it is also necessary to consider the relationship between man and machine.

Segmentation existed in the objective world before it was discovered, and it was only after the mystery was revealed that it became clearly understood.

When people look at the natural world according to this law, they are surprised to find that it can be seen in many beautiful things in nature, such as plant leaves, flowers, snowflakes, and five-pointed stars. The body structure of many animals and insects, especially in the human body, is rich in the best ratio.