There is a riddle: there is something invisible and intangible, but it is everywhere. What is this? The answer is: air. And mathematics, like air, is invisible and intangible, but it exists all the time around us.

Wonderful "golden numbers"

Take a line segment, find a point on the line segment, and let this point divide the line segment into two parts, one is long and the other is short, and the ratio of long segment to short segment is exactly equal to the ratio of whole segment to long segment. This point is the golden section of this line segment. This ratio is: 1: 0.6 18… and 0.6 18… This number is called "golden number".

Interestingly, this number can be seen everywhere in life: the navel is the golden section of the total length of the human body; The angle between two adjacent leaves on the stems of some plants is exactly the angle between the two radii that divide the circumference into 1: 0.6 18 …. According to research, this angle has the best effect on ventilation and lighting of the factory building.

Architects especially prefer the number 0.6 18 ... Whether it is the pyramids of ancient Egypt, Notre Dame de Paris or the modern Eiffel Tower, the number 0.6 18 ... It is also found that most of the subjects of some famous paintings, sculptures and photography are at the 0.618 ... Musicians believe that putting the bridge at 0.618 of the strings will make the sound softer and sweeter.

The number 0.6 18… also makes the optimization method possible. Optimization method is a method to solve the optimization problem. If it is necessary to add a chemical element to increase the strength of steel during steelmaking, it is assumed that the amount of a chemical element to be added per ton of steel is between 1000-2000g. In order to find the most suitable dose, we usually take the midpoint of the interval for experiments, and then compare it with the experimental results of 1000 g and 2000 g respectively, select two points with higher intensity as the new interval, and then take the midpoint of the new interval for experiments until the most ideal effect is obtained. However, this method is inefficient. If the measuring point is taken at the interval of 0.6 18, the efficiency will be greatly improved. This method is called "0.6 18 method". Practice has proved that the former method can be realized by using "0.6 18 method" to test 16.

There are so many examples and applications of "golden number" in life. Perhaps, there are more mysteries waiting for us to explore, so that it can serve us better and solve more problems for us.