Golden spiral is a kind of logarithmic spiral.
The formula of logarithmic spiral is: ρ = α e (φ k), where α and k are constants, φ is polar angle, ρ is polar diameter, and E is the base of natural logarithm.
When k=0.3063489 and the equal ratio P 1/P2=0.6 18 in the formula, the ratio of radii of adjacent poles on the same radius line in the helix has the golden section relationship. In fact, when the function f(X) is equal to the x power of e, let x be 0.48 12, then f(X)=0.6 18…, and the spiral formed in this way is the golden spiral, which has many beautiful features. Is the acme of acme, the beauty of China.
At the same time, it shows that the golden section law is contained in the logic of "natural law" based on e. In other words, "laws of nature" include the golden section.
The golden section law shows the relative static state of things, while the "natural law" shows the general state of the movement and development of things. Therefore, in a sense, the golden section law is a fixed "natural law" and the "natural section law" is a moving Huang Jinlv.
Make a square with three sides in the golden rectangle (the rectangle with the aspect ratio of 0.6 18), and the rest is the golden rectangle, which can be made into squares in turn. Connect the centers of these squares in turn and you can get a "golden spiral".
There have been rumors that "golden spirals" have been found in nautilus and some animals, such as horniness or mollusks with crustaceans.