Surprisingly, the human body itself is closely related to 0.6 18. Leonardo da Vinci, an Italian painter who is very good at human anatomy, found that human navel is located at 0.6 18 of body length. The throat is located at 0.6 18 of the length from navel to head; The elbow joint is located at 0.6 18 of the shoulder joint and finger length; The nose is located at 0.6 18 of the length from the top of the head to the chin. There are five golden acupoints in the human body, namely navel, throat, knee, elbow and nose, which are also the five keys to human survival.
The golden section is closely related to people. The latitude range of the earth's surface is 0-90 degrees. If divided into the golden section, 34.38-55.62 is the golden zone of the earth. No matter from the aspects of average temperature, annual sunshine hours, annual precipitation and relative humidity, it is the most suitable area for human life. Coincidentally, this region covers almost all the developed countries in the world.
Medicine is inextricably linked with 0.6 18, which can explain why people feel most comfortable in the environment of 22 to 24 degrees Celsius. Because human body temperature is 37℃, the product of 0.6 18 is 22.8℃, and the metabolism, circadian rhythm and physiological function of human body are in the best state at this temperature. Scientists also found that when the external environment temperature is 0.6 18 times of human body temperature, people will feel most comfortable. Modern medical research also shows that 0.6 18 is closely related to the way of keeping in good health, and the dynamic-static relationship is 0.6 18, which is the best way of keeping in good health. Medical analysis also found that people who eat 60% to 70% full will hardly have stomach problems.
In the elegant art hall, there are naturally golden footprints. The painters found that the ratio of leg length to height was 0.6 18: 1, and the figure they drew was the most beautiful. However, nowadays, the average length of women below the waist only accounts for 0.58 of their height. Therefore, the statue of Venus in ancient Greece and the image of Apollo, the sun god, deliberately put their legs out to make the ratio with their height reach 0.666. Thereby creating artistic beauty. No wonder many girls are willing to wear high heels, while ballerinas stand on tiptoe from time to time when dancing. Musicians found that when the chord ratio of "forward" is 0.618:1,the timbre played is the most harmonious and pleasant.
The leaves of plants are full of vitality, bringing a beautiful green world to nature. Although the shape of leaves varies from species to species, its arrangement order on the stem (called leaf order) is very regular. The growth of petals and branches on the trunk of some plants also conforms to this law. You look down from the top of the plant stem, and after careful observation, you find that the included angle between the upper and lower adjacent leaves is about 137.5. If only one leaf is drawn on each layer, the angle difference between two adjacent leaves on the first layer and the second layer is about 137.5, and the next two to three layers, three to four layers and four to five layers all form this angle. Botanists' calculations show that this angle is beneficial to the lighting of leaves. What is the "password" hidden in the angle of 137.5 between leaves? We know that a week is 360,360-137.5 = 222.5,137.5: 222.5 ≈ 0.618. Look, this is the "password"! The exquisite and magical arrangement of leaves actually hides 0.6 18.
The position of the solar system happens to be the golden section of the radius of the Milky Way.
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. Its ratio is an irrational number, 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.
0.6 18 is shorter than long, and 1.6 18 is his reciprocal.
You can draw the golden section on a triangle.
AB=2AC
∠A=90 degrees
Take c as the center, AC as the radius, and pass BC to D.
Then take B as the center, BD as the radius, and intersect AB at E..
AE:BE=0.6 18 ...............
And:
[(radical number 5)- 1]/2=0.6 18 ...............
2/[ (radical number 5)+1] =1.618 ............... [Edit this paragraph] The human body and the golden section contain many proportional factors of the golden section in the human body. At least 18 "golden points" can be found (for example, the umbilical cord is the dividing point from the top of the head to the sole of the foot, the Adam's apple is the dividing point from the top of the head to the umbilical cord, and the brow point is the dividing point from the hairline to the chin, etc. With the deepening of human understanding of nature (animals, plants, the universe and human beings themselves), human beings pay more and more attention to the "golden section"
The temperature is 37.5 degrees, and its product with 0.6 18 is 23. 175 degrees. Under this environmental temperature, the body's metabolism, circadian rhythm and physiological function are in the best state.
It is found that this magical proportion is almost everywhere in nature. From lower animals and plants to higher humans, from mathematics to astronomical phenomena, this proportional structure is almost implicit. It is found that the leaves of plants are full of vitality, bringing a beautiful green world to nature. Although the shape of leaves varies from species to species, its arrangement order on the stem (called leaf order) is very regular, not chaotic. You look down from the top of the plant stem, and after careful observation, you find that the included angle between the upper and lower adjacent leaves is about 137.5. If only one leaf is drawn on each layer, the angle difference between two adjacent leaves on the first layer and the second layer is about 137.5, and then two to three layers, three to four layers and four to five layers are all at this angle.
What is the "password" hidden in the angle of 137.5 between leaves? As we know, a week is 360 degrees,
360 - 137.5 =222.5
137.5 ∶222.5 ≈0.6 18.
Look, this is the "password"! The ingenious and magical arrangement of leaves actually hides 0.6 18, which accurately conforms to the golden section law in mathematics.
The same is true of pear trees, where leaves are arranged in logarithmic spiral, which also ensures that the leaves will not overlap, and the lower leaves are just in the gap where the upper leaves leak light, which is the arrangement mode with the largest lighting area. It can be seen that hovering along the logarithmic spiral according to the golden section of the circle is the best choice for blade arrangement.
A leaf also has the golden section phenomenon. The sum of the length of the main vein and petiole with the main vein is about 0.618; The spiral of sunflower disk and pine cone, the distribution of buds on plant stems, the development and formation of seeds and the growth formula of animal horns all follow the golden ratio. The geometry of the pyramid has five faces and eight sides, and the total number is thirteen layers. anyway/no matter what/ in any case
Looking inside, you can see three levels. The length of the pyramid is 58 13 inch (5-8- 13). Whether it is the Parthenon in ancient Greece or the Terracotta Warriors in ancient China, the ratio of vertical line to horizontal line is exactly 1 to 0.6 18. The aspect ratio of the front of Notre Dame de Paris is 8: 5, so is the aspect ratio of each window. The Oriental Pearl Radio and Television Tower on the east bank of Huangpu River is 468 meters high. Application of golden ratio in architectural design of new york United Nations Building. As we know, there are eight planets in the solar system at present. However, as early as the middle of18th century, German natural scientist Titius discovered that if every number in the series of 0, 3, 6, 12, 24, 48 and 96 is added with 4, and then divided by 10, the result is:
(0+4)÷ 10=0.4 (Mercury is actually 0.387 astronomical units away from the sun).
(3+4)÷ 10=0.7 (Venus is actually 0.723 astronomical unit from the sun).
(6+4)÷ 10= 1.0 (the actual distance from the earth to the sun is 1.000 astronomical units).
(12+4) ÷10 =1.6 (the actual distance from Mars to the sun is 1.524 astronomical unit).
(24+4)÷ 10=2.8 (asteroid belt)
(48+4)÷ 10=5.2 (Jupiter is actually 5.203 astronomical units from the sun).
(96+4)÷ 10= 10 (Saturn is actually 9.56 astronomical units from the sun).
By comparing the above figures, we can see that the value calculated by Titius is really very close to the actual distance between the planet and the sun. 1766, when Titius translated the book Exploring Nature from French into German, he also added this rule he discovered to the book by the way. However, after the book was published, it did not attract people's general attention. 1772, Bode of the Berlin Observatory noticed this strange law and wrote it into the book "A Guide to Starry Sky Research" to introduce it. This is the Titius-Bode rule often mentioned by later generations. But what needs to be explained is: Why are the numbers 0, 3, 6, 12, 24, 48 added by 4 and then divided by 10, but not other numbers? Neither Titius nor Bode gave any explanation. What's the mystery in this? Neither of them explained.
In recent years, someone has used the golden section method to calculate the distance between the planet and the sun, and the result is equally surprising!
0.732× 0.6 18 = 0.446 (Mercury is actually 0.387 astronomical unit from the sun).
1.000× 0.618 = 0.618 (Venus is actually 0.723 astronomical units away from the sun).
1.52× 0.6 18 = 0.939 (the actual distance from the earth to the sun is 1.000 astronomical unit).
2.80× 0.6 18 = 1.73 (the actual distance from Mars to the sun is 1.52 astronomical unit).
5.20× 0.6 18 = 3.2 13 (the asteroid belt is actually 2.8 astronomical units away from the sun).
9.54× 0.6 18 = 5.89 (Jupiter is actually 5.2 astronomical units away from the sun).
19.2× 0.618 =11.86 (Saturn is actually 9.54 astronomical units away from the sun).
30.1× 0.618 =18.605438+0 (actual distance of Uranus from the sun 19.2 astronomical unit).
: 1 astronomical unit is equal to1.500 million kilometers.
From the above picture, we can see that apart from the actual distance error between Saturn and the sun, other planets are still very close to the sun. If the mutual attraction and eccentricity between planets are considered, the calculated value will be more accurate. For example, Saturn is not only attracted by the sun, but also influenced by Jupiter's great gravity, so it is not difficult to understand that its actual distance is less than the calculated value. Of course, using the golden section method to calculate the distance between the planet and the sun, like the Titius-Bode rule, is challenged in the calculation of Neptune and Pluto, and the reasons need further analysis and research.
As we know, the Milky Way is a huge celestial system, in which stars account for 90% and gas and dust account for 10%. Most of these substances gather near the central plane and run around the center of the Milky Way. Viewed from the side, our Milky Way looks like a flat discus, with an overall diameter of 25,000 parsec to 30,000 parsec, while our earth and solar system are 85,000 parsec away from the center of the Milky Way. In recent years, it has been found that the location of our solar system is also the golden section of the radius of the Milky Way. Namely: 27.5 ÷ 2× 0.6 18 = 8.4975 (thousands of parsec).