In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion.
When Euclid wrote Pacioli around 300 BC, he absorbed eudoxus's research results and further systematically discussed the golden section, which became the earliest treatise on the golden section.
After the Middle Ages, the golden section was cloaked in mystery. Several Italians, pacioli, called the ratio between China and the destination sacred and wrote books on it. German astronomer Kepler called the golden section sacred.
It was not until the19th century that the name golden section gradually became popular. The golden section number has many interesting properties and is widely used by human beings. The most famous example is the golden section method or 0.6 18 method in optimization, which was first proposed by American mathematician Kiefer in 1953 and popularized in China in 1970s.
Interestingly, this number can be seen everywhere in nature and people's lives: the navel is the golden section of the whole human body, and the knee is the golden section from the navel to the heel. The aspect ratio of most doors and windows is also 0.618. On some plants, the included angle between two adjacent petioles is 137 degrees 28', which is exactly the included angle between 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 have a special preference for 0.6 18… in mathematics. No matter the pyramids in ancient Egypt, Notre Dame de Paris, or the Eiffel Tower in France in recent centuries, there are data related to 0.6 18 … It is also found that the themes of some famous paintings, sculptures and photos are mostly at 0.6 18…. The artist thinks that placing the bridge of a stringed instrument at the position of 0.6 18 can make the sound softer and sweeter.
The number 0.6 18 ... is more concerned by mathematicians. Its appearance not only solves many mathematical problems (such as dividing the circumference into ten parts and dividing the circumference into five parts; Find the sine and cosine values of 18 degrees and 36 degrees. ), it 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 added per ton of steel is between1000-2000g. In order to find the most suitable dosage, it needs to be tested between 1000 g and 2000 g. Usually take the midpoint of the interval (i.e. 1500g) for testing. Then compared with the experimental results of 1000g and 2000g respectively, two points with higher intensity were selected as new intervals, and then the midpoint of the new interval was taken for experiments, and the endpoints were compared in turn until the most ideal results were obtained. This experimental method is called dichotomy. However, this method is not the fastest experimental method. If the experimental point is 0.6 18 of the interval, the number of experiments will be greatly reduced. This method of taking 0.6 18 of the interval as the test point is a one-dimensional optimization method, also known as 0.6 18 method. Practice has proved that for the problem of one factor, using "0.6 18 method" to do 16 experiments can complete the effect of "dichotomy" to do 2500 experiments. So Da Vinci, the great painter, called 0.618 ... the golden number.
0.6 18 and strategic campaign
0.6 18 is an extremely fascinating and mysterious number, and it also has a very nice name-the golden section law, which was discovered by Pythagoras, a famous ancient Greek philosopher and mathematician, more than 2,500 years ago. Throughout the ages, this number has been regarded as the golden rule of science and aesthetics by future generations. In the history of art, almost all excellent works have verified this famous golden section law. Whether it is the Parthenon in ancient Greece or the Terracotta Warriors in ancient China, the ratio of vertical line to horizontal line is exactly 1 to 0.6 18.
Perhaps, we have learned a lot about the performance of 0.6 18 in science and art, but have you ever heard that 0.6 18 has an indissoluble bond with the fierce and cruel battlefield of gunfire and bloodshed, and also shows its great and mysterious power in the military?