The golden ratio is a proper term in the field of mathematics, but it ultimately covers more than just the research in the field of mathematics. According to the current literature, we can say that the discovery and evolution of the golden section ratio is still a mystery.
However, some studies have pointed out that the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular 10 polygons in the 6th century BC, so modern mathematicians have come to the conclusion that Pythagoras school contacted and even mastered some laws of the golden section at that time, and also discovered irrational numbers.
He mainly discusses the law of beauty from the mathematical relationship, and thinks that beauty is harmony and proportion. According to this proportional relationship, beautiful patterns can be formed. This is actually a numerical proportional relationship, that is, a line is divided into two parts, and the ratio of long segment to short segment is equal to the ratio of full length to long segment, and their ratio is about1.618:1;
The well-known Fisher series also embodies this mathematical principle, and everything composed according to this proportional relationship shows the harmony and balance of its internal relationship.
In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion. When Euclid wrote The Elements of Geometry 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 (that is, the comparison between the middle and the end).
After the Middle Ages, the golden section was covered by mystery. Italian mathematician luca pacioli called the ratio between China and the destination sacred and wrote a book about it.
German astronomer johannes kepler called this sacred ratio the golden section. It was not until the19th century that the name "golden section" gradually became popular. The evidence lies in the explanation of the golden ratio in the second edition of Basic Pure Mathematics written by German mathematician Martin Ohm: "People are used to dividing any straight line into two parts in this way, which is called the golden section".
In the ninth edition of Encyclopedia Britannica published in 1875, Su Li mentioned: "Ferdinand put forward an interesting and experimental idea, claiming that the golden section has the so-called superiority in visual proportion." It can be seen that the golden section was popular at that time. In the 20th century, American mathematician Mark Barr named it phi.
The golden section has many interesting properties and its practical application is very extensive, which makes it famous today. The most famous example is the golden section method or 0.6 18 method in optimization, which was first proposed by American mathematician Jack Kiefer in 1953 and popularized in China in 1970s.
Application example
The golden section has strict proportionality, artistry, harmony and rich aesthetic value, which can arouse people's aesthetic feeling and is considered as the most ideal proportion in architecture and art.
The painters found that the painting with the ratio of 0.6 18: 1 was the most beautiful, and the golden section was used in Leonardo da Vinci's works Vitruvian Man, Mona Lisa and The Last Supper.
Nowadays, the average length of women below the waist only accounts for 0.58 of their height, so Venus, the famous statue of broken arm in ancient Greece, and Apollo, the sun god, specially lengthened their legs to make their ratio to their height 0.6 18.
Architects especially prefer the number 0.6 18. Whether it is the pyramids in ancient Egypt, Notre Dame de Paris, the Eiffel Tower in France in the past century, or the Parthenon in Athens, Greece, there are footprints of the golden section.