What is the demarcation point of gold?

"Infinite! No other problem has touched the human mind so deeply. " Some people say that the golden section is an infinitely magical section, and 0. 18 is also an infinitely wonderful golden number.

1. golden section

Divide a line segment AB into two segments, AB MB, so that the longer line segment AM is the median of the ratio of the total length AB to the shorter line segment MB, that is, AB:AM=AM:MB. We call this division the golden section, and vernal equinox M is called the golden section.

2. Gold index

According to the definition, line segment AB and MB have the following relationship: AM2=AB×MB, let AB= 1, AM=X, then MB = 1-

X, so there is

X2 = 1× (1-x), that is, x2+x- 1 = 0.

Solve the equation and remove the negative root, X=(5 square root-1)/2 ≈ 0.6 18.

We call 0.6 18 the golden number, golden ratio, golden ratio, Chinese-foreign ratio and Chinese-foreign ratio.

The "golden section" was first discovered by the Pythagorean school, an ancient Greek mathematician, more than 2,000 years ago when studying the painting methods and properties of regular pentagons. The name "golden section" was created by Italian artist Le Aldo? Da? Finch gave it to me. 1607, Xu Guangqi and Matteo Ricci jointly translated The Elements of Geometry and introduced this method to China.

3. The art of golden section

Leonardo da vinci has extensively studied various proportions of the human body. The picture below shows his detailed study of the human body, which shows the application of the golden section. This is his illustration for the book "Magic Proportion" by mathematician L pacioli published in 1509.