(1) The golden section law was discovered by Pythagoras, an ancient Greek mathematician in the 6th century BC, and later called it the golden section by Plato, an ancient Greek aesthete. This is actually a numerical proportional relationship, that is, dividing a line into two parts. At this time, the ratio of long segment to short segment is exactly equal to the ratio of the whole line to long segment, and its numerical ratio is 1.6 18: 1 or 1: 0.6 18, that is to say, long. 0.6 18, with strict proportionality, artistry and harmony, contains rich aesthetic value. Why do people instinctively feel the existence of beauty for such a proportion? In fact, this is closely related to the evolution of human beings and the normal development of human bodies. According to research, in the process of evolution from apes to humans, the skull and leg bones changed the most and the body shape changed the least, because it was similar to gold. Many proportions in the human body structure are close to 0.6 18, so the beauty of the human body is fixed in the historical accumulation of hundreds of thousands of years. Humans are most familiar with themselves, and they will inevitably regard the beauty of the human body as the highest aesthetic standard, which is derived from things and people and from people and things. Any object similar to the human body likes it and feels beautiful. Therefore, the golden section law, as an important law of formal beauty, has become an aesthetic classic law handed down from generation to generation, and it has never failed! In recent years, when studying the relationship between the golden section and the human body, it has been found that there are 14 "golden points" (the ratio of short segment to long segment of an object is 0.6 18), 12 "golden rectangles" (the width-length ratio is 0.6 18) and two "golden rectangles".

The exact value of the golden section law is (√5- 1)/2, which is the golden section number.

The golden section number is irrational, and the first 1024 bits are:

0.6 180339887 4989484820 4586834365 638 1 177203 09 17980576

2862 135448 6227052604 628 1890244 9707207204 18939 1 1374

8475408807 538689 1752 1266338622 2353693 179 3 180060766

7263544333 8908659593 9582905638 32266 13 199 2829026788

0675208766 89250 17 1 16 9620703222 10432 16269 5486262963

136 14438 14 975870 1220 3408058879 5445474924 6 185695364

86444924 10 4432077 134 4947049565 8467885098 743394422 1

2544877066 47809 15884 607499887 1 24007652 17 0575 179788

34 16625624 9407589069 70400028 12 1042762 177 1 1 17778053

153 17 14 10 1 1704666599 1466979873 176 1356006 70874807 10

13 17952368 942752 1948 4353056783 0022878569 9782977834

7845878228 9 1 10976250 0302696 156 1700250464 3382437764

86 1028383 1 2683303724 292675263 1 1653392473 167 1 1 12 1 15

88 186385 13 3 162038400 5222 16579 1 2866752946 549068 1 13 1

7 159934323 5973494985 0904094762 1322298 10 1 726 1070596

1 164562990 98 16290555 2085247903 52406020 17 2799747 175

3427775927 786256 1943 20827505 13 12 18 156285 5 122248093

947 1234 145 1702237358 05772786 16 0086883829 5230459264

78780 17889 92 19902707 7690389532 1968 1986 15 1437803 149

974 1 106926 0886742962 2675756052 3 172777520 3536 139362

1076738937 6455606060 5922 ...

14 "golden part" of human body:

Navel: the dividing point between the top of the head and the bottom of the foot;

Throat: the dividing point between the top of the head and the navel;

(3), (4) Knee joint: the dividing point between navel and sole;

(5) and (6) Elbow joint: the dividing point between shoulder joint and middle fingertip;

(7) and (8) nipple: the dividing point on the longitudinal axis of trunk nipple;

(9) Eyebrow point: the dividing point between hairline and chin base 1/3 and 2/3;

(10) Subnasal point: the dividing point between hairline and chin base 1/3 and 2/3;

(1 1) lip bead point: the dividing point between the nose base and the chin base 1/3 and the middle and lower 2/3;

(12) straight point of chin labial groove: the dividing point between 1/3 and upper middle 2/3 is the distance between nose base and chin base;

(13) Left corner point: the boundary point between the left 1/3 and the right 2/3 of the horizontal line of the oral fissure;

(14) Right corner point: the boundary point between the right 1/3 and the left 2/3 of the horizontal line of the oral fissure.

12 "golden rectangle" of human body

(1) Body contour: shoulder width, hip breadth average width, and height from acromion to buttock base;

(2) Facial contour: the horizontal face of eyes is wide, and the distance from hairline to the bottom of chin is long;

(3) Nose contour: the alar is wide and the distance from the nasal root to the nasal floor is long;

(4) Lip contour: At rest, the distance between the peaks of the upper and lower lips is wider, and the distance between the lips is longer;

(5) and (6) Hand contour: the transverse diameter of the hand is wide, and the average length is taken when the five fingers are together;

(7), (8), (9), (10), (1 1), (12) Maxillary incisors, lateral incisors and canine profiles (three on the left and three on the right): the largest mesial and distal diameters.

Two "golden indexes":

(1) Nose-lip index reflecting the relationship between nose and mouth: the ratio of alar width to spat spacing is close to the golden number;

(2) Eye-lip index reflecting the relationship between eyes and mouth: the ratio of the distance between the corners of the mouth and the outer canthus of the eyes is close to the golden number.

As one of the standard scales of bodybuilding, 0.6 18 is beyond reproach, but it has "fuzzy characteristics". Like other aesthetic parameters, it has an allowable range of change, which is restricted by ethnic, regional and individual differences.

(2) The proportional relationship is to express the beauty of the human body with figures and compare them according to certain benchmarks. The method of judging the proportional relationship between a certain part of the same human body and the human body is called the same body method (see the middle picture). Divided into three groups: coefficient method, constant finger height and length index, such as human body sitting five times and standing seven times, that is, the height is five times the height of head when sitting, and 7 or 7.5 times when standing; Percentage method, the body length is regarded as 100%, and the proportion of all parts of the body in it; Dichotomy: that is, the human body is divided into two parts, most of which are from the foot to the navel, and a small part is from the navel to the top of the head. Standard face, its length-width ratio is coordinated, which accords with three stops and five eyes (see the right picture). Three stops refers to the length of the face, and the distance from the hairline of the head to the chin is divided into three equal parts, that is, from the hairline to the eyebrows, from the eyebrows to the tip of the nose, and from the tip of the nose to the chin. Each equal part is called one stop and three stops; Five eyes refers to the width of the face, and the frontal projection length between the two ears is the length of five-eye fissure. Except for eye fissure, the distance between the inner canthus and the outer canthus on both sides is the length from one eye fissure to the ear.

(for reference)

The golden section of the earth

There is a mysterious zone near the Tropic of Cancer, which is famous for its rich natural mysteries. For example, the mystery of the famous pyramids, the mystery of the formation of the Dead Sea, the mystery of the Bermuda Triangle, and the mystery of the tilt of Santa Cruz Town are just one of many mysteries. A simple survey on the map shows that this area is exactly in the golden ratio of the earth -0.6 18. This strange geometric ratio seems to be the code word of God.

In foreign exchange technology, the golden section ratio of 0.382 0.50.6 18 is the most important, while the latter ratio is only a small part of the supporting role, and the probability of occurrence is far less than these three ratios.