First, the definition of the golden ratio.
The golden ratio is usually expressed by the Greek letter φ(phi), and its value is about 1.5438+0987. This is an infinite acyclic decimal, which is considered to be one of the most attractive and harmonious proportions in aesthetics and art.
Secondly, the algorithm of golden section rate.
The calculation method of the golden ratio can be carried out according to the following steps: assuming that the total length is L and the length of the longer part is X, the length of the shorter part can be obtained by subtracting the length of the longer part from the total length, that is, L-X. According to the definition of the golden ratio, we have the following equation: X/(L-X) = L/X.
Convert the fraction in the equation into proportional form, and get X/L-X = L/X. The permutation equation, and get X 2-LX+L 2 = 0. Use the quadratic equation to find the root formula, and calculate the value of X = (L √ (L 2-4L 2))/2 Note: Because the golden ratio is proportional, the value of X calculated according to the formula is only a relative ratio, and the specific value needs to be adjusted according to the actual situation.
Expand knowledge:
The golden ratio was widely used in ancient Greece and was considered to be a perfect and harmonious ratio. It is widely used in architecture, art, design and other fields, such as building design, composition of painting and sculpture, rhythm and melody of music and so on.
The golden ratio can also be derived from other geometric shapes, the most famous of which are the golden rectangle and the golden spiral. Golden rectangle refers to a rectangle with an aspect ratio close to the golden section ratio, which has a sense of visual harmony. The golden spiral is a special spiral, and the ratio of the long axis to the short axis of each cycle is also close to the golden ratio.
Summary:
The golden ratio means that when a line segment is divided into two parts, the ratio of the longer part to the whole is equal to the ratio of the shorter part to the longer part. Its calculation method can be solved by the root formula of quadratic equation. The golden ratio is widely used in aesthetics and art, and there are many examples of the golden ratio in nature.