What is the ratio of normal leg length to height?

Answer:105.6cm. (The perfect leg length at the golden section) 170cm times 0.6 18 is your perfect leg length. 105.6cm~

When dividing, the length is about 0.6 18, which is called golden section. This demarcation point is called the golden section.

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, expressed as a fraction (√5- 1)/2, 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, which is expressed by 0.6 18. Through simple calculation, we can find that:

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.

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.

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.

Since the vertex angle of the five-pointed star is 36 degrees, it can also be concluded that the golden section value is 2Sin 18 degrees.

The golden section is approximately equal to 0.6 18: 1.

It refers to dividing a line segment 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 other part. The simplest way to calculate the golden section is to calculate Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 2 1, ... and then 2/3, 3/5, 4/8, 8/65438.

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 1.6 18 in application, just as pi is 3. 14 in application.

Discover history

Since the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC, modern mathematicians have come to the conclusion that Pythagoras school had touched and even mastered the golden section at that time.

In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion.

When Euclid wrote The Elements of Geometry around 300 BC, he absorbed eudoxus's research results and further systematically discussed the golden section, which became the earliest treatise on the golden section.

After the Middle Ages, the golden section was cloaked in mystery. Several Italians, pacioli, called the ratio between China and the destination sacred and wrote books on it. German astronomer Kepler called the golden section sacred.

It was not until the19th century that the name golden section gradually became popular. The golden section number has many interesting properties and is widely used by human beings. The most famous example is the golden section method or 0.6 18 method in optimization, which was first proposed by American mathematician Kiefer in 1953 and popularized in China in 1970s.

|..........a...........|

+ - + - + -

| | | .

| | | .

| B | A | b

| | | .

| | | .

| | | .

+ - + - + -

|......b......|..a-b...|

This value is usually expressed in Greek letters.

The wonder of the golden section is that its proportion is the same as its reciprocal. For example, the reciprocal of 1.6 18 is 0.6 18, while1.618 is the same as 1:0.6 18.

The exact value is (root number 5+ 1)/2.

The golden section number is irrational, and the top 2000 digits are:

0.6 180339887 4989484820 4586834365 638 1 177203 09 17980576 : 50

2862 135448 6227052604 628 1890244 9707207204 18939 1 1374 : 100

8475408807 538689 1752 1266338622 2353693 179 3 180060766 : 150

7263544333 8908659593 9582905638 32266 13 199 2829026788 : 200

0675208766 89250 17 1 16 9620703222 10432 16269 5486262963 : 250

136 14438 14 975870 1220 3408058879 5445474924 6 185695364 : 300

86444924 10 4432077 134 4947049565 8467885098 743394422 1 : 350

2544877066 47809 15884 607499887 1 24007652 17 0575 179788 : 400

34 16625624 9407589069 70400028 12 1042762 177 1 1 17778053 : 450

153 17 14 10 1 1704666599 1466979873 176 1356006 70874807 10 : 500

13 17952368 942752 1948 4353056783 0022878569 9782977834 : 550

7845878228 9 1 10976250 0302696 156 1700250464 3382437764 : 600

86 1028383 1 2683303724 292675263 1 1653392473 167 1 1 12 1 15 : 650

88 186385 13 3 162038400 5222 16579 1 2866752946 549068 1 13 1 : 700

7 159934323 5973494985 0904094762 1322298 10 1 726 1070596 : 750

1 164562990 98 16290555 2085247903 52406020 17 2799747 175 : 800

3427775927 786256 1943 20827505 13 12 18 156285 5 122248093 : 850

947 1234 145 1702237358 05772786 16 0086883829 5230459264 : 900

78780 17889 92 19902707 7690389532 1968 1986 15 1437803 149 : 950

974 1 106926 0886742962 2675756052 3 172777520 3536 139362 : 1000

1076738937 6455606060 592 1658946 675955 1900 4005559089 : 1050

5022953094 23 12482355 2 122 124 154 4400647034 0565734797 : 1 100

6639723949 4994658457 8873039623 0903750339 938562 1024 : 1 150

2369025 138 6804 145779 95698 12244 5747 178034 173 1264532 : 1200

204 1639723 2 134044449 4873023 154 1767689375 2 103068737 : 1250

880344 1700 9395440962 7955898678 7232095 124 2689355730 : 1300

9704509595 68440 17555 1988 192 180 2064052905 5 189349475 : 1350

9260073485 2282 10 1088 1946445442 223 1889 13 1 9294689622 : 1400

00230 14437 7026992300 780308526 1 1807545 192 88770502 10 : 1450

9684249362 7 135925 187 6077788466 5836 150238 9 13493333 1 : 1500

223 1053392 32 136243 19 2637289 106 7050339928 2265263556 : 1550

2090297986 4247275977 25655086 15 4875435748 2647 18 14 14 : 1600

5 127000602 3890 162077 7322449943 5308899909 50 1680328 1 : 1650

12 19432048 1964387675 8633 147985 7 19 1 13978 1 5397807476 : 1700

1507722 1 17 5082694586 3932045652 0989698555 678 14 10696 : 1750

8372884058 746 103378 1 0544439094 368358358 1 38 1 13 1 1689 : 1800

9385557697 5484 149 144 534 1509 129 54070050 19 4775486 163 : 1850

07542264 17 2939468036 73 1980586 1 8339 183285 99 13039607 : 1900

20 14455950 4497792 120 76 12478564 59 16 160837 0594987860 : 1950

06970 18940 9886400764 436 1709334 172709 19 14 33650 137 15 : 2000

We often hear the word "golden section". Of course, "golden section" does not mean how to divide gold. This is a visual statement that the proportion of points is as precious as gold. So what's the ratio? It is 0.6 18. People call the dividing point of this ratio the golden section point and 0.6 18 the golden section number. And people think that if it meets this ratio, it will look more beautiful, more beautiful and more harmonious. In life, "golden section" has many applications.

The most perfect human body: the distance from navel to sole/the distance from top of head to sole =0.6 18.

The most beautiful face: the distance from eyebrow to neck/the distance from the top of head to neck =0.6 18.

When making steamed bread, the ratio of baking powder to flour is 0.6 18, which makes the steamed bread the most delicious.

I forgot the password of a number before ~ that number has many points ~ ~ ```````` This number is my new application. Please give some points ~ thank you.