Is the golden section a fixed value? It's 0.618

Is the golden section a fixed value? It's 0.618

The exact value is (√ 5-1) / 2, that is, the golden section number, which is generally taken as 0.618 in application, just as the PI is taken as 3.14 in application
Yes. But it's not rational.
yes.
golden section
Golden section was first seen in ancient Greece and ancient Egypt. Golden section, also known as golden ratio and ratio of middle to outer, divides a line segment into a and B segments with different lengths, so that the ratio of long segment (a + b) is equal to the ratio of short segment B to long segment a. the formula is a: (a + b) = B: A, and the ratio is 0.6180339 This ratio is more pleasing to the eye in modeling, therefore, 0.618 is also known as the golden ratio. The golden section rectangle itself is composed of a square and a golden section rectangle. You can divide these two basic shapes infinitely
golden section
Golden section was first seen in ancient Greece and ancient Egypt. Golden section, also known as golden ratio and ratio of middle to outer, divides a line segment into a and B segments with different lengths, so that the ratio of long segment (a + b) is equal to the ratio of short segment B to long segment a. the formula is a: (a + b) = B: A, and the ratio is 0.6180339 This ratio is more pleasing to the eye in modeling, therefore, 0.618 is also known as the golden ratio. The golden section rectangle itself is composed of a square and a golden section rectangle. You can divide these two basic shapes infinitely. Because its own proportion can produce moderate stimulation to people's vision, its length proportion is just in line with people's visual habits, so it makes people feel pleasant. Golden section is widely used in architecture, design, painting and other aspects. In the development of photography technology, the essence of other art classes has been borrowed from different degrees, and the golden section has become the most sacred concept in photographic composition. The simplest way to use it in photography is to arrange the numbers 2, 3, 5, 8, 13, 21 according to the golden ratio of 0.618 The ratio of 2:3, 3:5, 5:8, 8:13, 13:21 can be obtained. These ratios are approximate values of 0.618. These ratios are mainly applicable to the determination of the aspect ratio of the picture (for example, the negative format of 135 camera is 24mmx36mm, which is derived from the golden ratio), the selection of horizon position, the distribution of light and shadow tones, the division of picture space, and the visual center of the picture The establishment of the system. The three division method commonly used in photographic composition (also known as well as well shaped segmentation method) is the evolution of golden section. The length and width of the upper square picture are divided into three equal parts, and the whole picture bears well shaped segmentation. The intersection of well shaped segmentation is the best position of the main body (visual center) of the picture, which is the visual beauty that most easily induces people's visual interest. Many basic laws of photographic composition are evolved from the golden section. However, it is worth noting that every picture does not need and cannot be completely composed according to the golden section. It's monotonous and boring to be the same. On the golden section, it is important to master its laws and apply them flexibly. Put it away
We have learned four methods of solving quadratic equation of one variable: factorization, flattening, collocation and formula. Please choose the appropriate method to solve the following four equations. (1) x2-3x + 1 = 0; (2) (x-1) 2 = 3; (3) x2-3x = 0; (4) x2-2x = 4
（1）x2-3x+1=0，x=3±9-42=3±52，x1=3+52，x2=3-52；（2） （x-1）2=3，x-1=±3，x1=1+3，x2=1-3；（3） x2-3x=0，x（x-3）=0，x1=0，x2=3；（4） x2-2x=4，x2-2x+1=4+1，（x-1）2=5，x-1=±5，x1=1+5，x2=1-5．...
Why is the golden section 0.618?
A line segment is divided into two parts, so that the ratio of one part to the whole length is equal to the ratio of the other part to this part. The ratio is 5 ^ / 2-1 / 2 or the root of two is five minus one, and the approximate value of the first three digits is 0.618
There are three ways to solve quadratic equation of one variable: collocation method, formula method and factorization method. What kind of equation are these methods suitable for?
You can try the above method
But the formula method is used in the other two cases
How do you get the golden section of 0.618?
In the 13th century, the mathematician fabrance wrote a book about the combination of some singular numbers. The combination of these singular numbers is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233... Any number is the sum of the first two numbers, 2 = 1 + 1, 3 = 2 + 1, 5 = 3 + 2, 8 = 5 + 3, Some people say that these figures are derived from his study of pyramids. Pyramids are closely related to the strange numbers listed above. The geometric shape of pyramids has five sides, eight sides, and a total of 13 levels. If you look at them from any side, you can see three levels. The length of pyramids is 5813 inches (5-8-13), and the percentage of high bottom and bottom is 0.618, That is any two consecutive ratios of the above mysterious numbers, for example, 55 / 89 = 0.618, 89 / 144 = 0.618, 144 / 233 = 0.618. In addition, the length of any side of a pyramid pentagonal tower is equal to 0.618 of the Pentagon diagonal, The reciprocal of 0.618 is 1.618. For example, 144 / 89 = 1.168, 233 / 144 = 1.168, and 0.618 × 1.618 = 1. In addition, someone has studied sunflowers and found that they have 89 braids, 55 on one side and 34 on the other, 1.618 is called the golden section
A line segment is divided into two parts so that the ratio of one part to the whole length is equal to the ratio of the other part to this part. The ratio is five minus one, and the approximate value of the first three digits is 0.618.
(radical 5-1) / 2
Among the three methods of collocation method, formula method and factorization method, choose the simplest one to solve
x²－4√2+9=0 5+x+16x²=15x²-3x+1
x²-x+7／4=0 （x-3）²=（5-2x）²
(1) Formula method
(2) Transfer term, get: X & # 178; + 4x + 4 = 0
(3) Formula method
(4) Direct leveling method: x-3 = ± 5-2x
The golden ratio of 1:0.618 refers to the proportion of which part of the hair
The ratio is [5 ^ (1 / 2) - 1] / 2, and the approximate value of the first three digits is 0.618. Because the shape designed according to this ratio is very beautiful, it is called golden section, also known as the ratio of middle to outer
The line from the golden point to the two ear points is the golden line. Before and after the golden line is 1: 0.618
navel
It is known that the two roots of the quadratic equation x2 + BX + C = 0 with real coefficients of X are x1, X2, and satisfy the relation (1-3bi) I = c-bi (I is an imaginary unit). (1) find the value of B, C; (2) find the two roots of the equation x1, x2
(1) Let (1-3bi) I = c-bi, that is: - (1-3bi) = ci-b, get 1 = B3b = C, solve B = 1, C = 3, (2) substitute B = 1, C = 3 in (1) into equation x2 + BX + C = 0, get: x2 + X + 3 = 0, find out two imaginary roots as X1 = - 1 + 11i2, X1 = - 1-11i2
What is the application of golden section 0.618 in music
The most famous buildings in the world almost all contain "golden section ratio". Whether it is ancient Egyptian pyramids, ancient Greek Parthenon temple, ancient Egyptian pyramid of Hoover, India's Taj Mahal, the Forbidden City of China, Notre Dame of Paris, these famous ancient buildings, or many excellent modern buildings all over the world
Write out a quadratic equation with one variable by factorization, so that its roots are - 3 and 6
For example: y = (x + 3) (X-6)