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How was the golden section discovered?
The mathematician Fabrance wrote a book about some strange combinations of numbers in the13rd century. The combination of these strange numbers is 1, 1, 2,3,5,8,13,21,34,55,89,144,233. ...

Any number is the sum of the first two numbers. 2 = 1+ 1, 3 = 2+ 1, 5 = 3+2, 8 = 5+3 and so on.

Some people say that he got these figures by studying the pyramids. The pyramids are closely related to these strange numbers. The geometry of the pyramid has five faces and eight sides, and the total number is thirteen layers. From any side, you can see three levels. The length of the pyramid is 5,865,438+03 inches (5-8-65,438+03), and the percentage of high bottom and bottom is 0.665,438+08, which is the ratio of any two consecutive mysterious numbers mentioned above, for example, 55/89 = 0.665,438+08,800. In addition, the length of any side of a pentagonal pyramid is equal to 0.6438+08 of the diagonal of the pentagonal pyramid.

This set of figures is very interesting. The reciprocal of 0.6 18 is 1.6 18. For example,144/89 =1.618,233/144 =1.618,0.618. These numbers are full of mystery, so they are called mysterious numbers. While 0.6 18 and 1.6 18 are called the golden section.

For hundreds of years, some scholars and experts have found that architectural structure, mechanical engineering, music art, and even many natural things are all related to the mysterious numbers of 0.382 and 0.6 18 with an approximate ratio of "5: 8". Because the mysterious numbers 0.382 and 0.6 18 add up to 1, the ratio of 0.382 and 0.6 18 is called "golden ratio" or "golden ratio".

Many experts and scholars have pointed out that the "golden ratio" not only has an aesthetic point of view, but also has the purpose of realizing functions. Such as buildings, picture frames, playing cards and books. The length-width ratio is very close to the "golden ratio". For another example, the length from the navel to the sole of the foot accounts for about 0.6 18 of the whole body length, and the figure must be symmetrical. For another example, the rate of bacterial reproduction, the fluctuation of sea waves, the rotation of hurricane clouds and outer space nebulae are all related to the ratio of 1.6 18 times of the "golden spiral" extended by the "golden ratio".