For centuries, a great deal of knowledge has been accumulated around phi, for example, it represents perfect beauty or unique discoveries in nature. But this is mostly unfounded in reality.
Phi phi can be defined by dividing a stick into two parts. If the ratio between these two parts is the same as that between the whole stick and the larger part, these parts are called the golden ratio, which was first described by the Greek mathematician Euclid, although he called it "division of extreme average ratio". According to George Macovschi, a mathematician at the University of Maine,
You can also think that phi is a number, and this number can be squared by adding a number. According to mathematicians, Ron Knodt is at the University of Surrey in England. So PHI can be expressed as follows: "KDSP", "kdsp" φ 2 = φ+1"kdsp" and "kdsp", which can be rearranged into a quadratic equation. The first solution leads to a positive irrational number1.66538+0803383831... (the point represents the number forever), commonly known as phi. The negative solution is -0.6 180339887. . . (Notice how the numbers after the decimal point are the same) Sometimes it is called small phi.
The last quite elegant way to express phi is as follows:
5^0.5*0.5+0.5
This is half of the fifth power, multiply by half and add half.
Related: 1 1 The most beautiful mathematical equation
Phi is closely related to Fibonacci sequence. In Fibonacci series, each subsequent number in the series is obtained by adding the first two numbers. This order is 0, 1, 1, 2, 3, 5, 8, 13, 2 1, 34 and so on. It is also related to many misunderstandings.
By calculating the ratio of continuous Fibonacci numbers, we can get closer and closer to phi. Interestingly, if you reverse the Fibonacci series, that is, turn it into a negative number before 0, the ratio of these numbers will make you get closer and closer to the negative solution, and the smaller φ 0.6 18039887 ... Is there a golden ratio in KDSPE in nature?
"Although people have known about phi for a long time, it didn't become famous until recent centuries. According to Nott, luca pacioli, an Italian mathematician in the Renaissance, wrote a book called De Divina Provo in 1509, discussing and popularizing phi.
Pacho used paintings with phi painted by Leonardo da Vinci. It is possible that Leonardo da Vinci was the first person to call it the "Golden Festival". It was not until19th century that American mathematician Mark Barr used the Greek letter φ (PHI) to represent this number.
Other names of this number, such as sacred proportion and golden section, prove that many wonderful attributes are attributed to phi. Dan brown, a novelist, added a long passage to his best-selling book Doubleday (2000), in which the hero discussed how phi represents the ideal of beauty, which runs through the whole history. More sober scholars often debunk such assertions.
For example, phi lovers often mention that some measured values of great pyramid of giza, such as the length and/or height of its bottom, are the golden ratio. Others claimed that the Greeks used phi when designing the Parthenon or their beautiful statues.
Phi lovers like to point out that the Pyramid of Giza was built from 2589 to 2504 BC, and it was built according to the golden ratio. But the measurement itself is inaccurate and arbitrary, so the pyramid is not an accurate example of the golden ratio. The title is "misunderstanding of the golden ratio": "the measurement of physical objects can only be approximate." The surface of a real object is never completely flat. "He went on to write that when these measured values are converted into proportions, the inaccuracy of measurement accuracy will lead to greater inaccuracy. Therefore, the idea of ancient architecture or art that conforms to phi should be measured by heavy salt. The size of architectural masterpieces is usually considered to be close to phi, but as discussed by Macovschi, sometimes this means that people just need to find a ratio of 1.6 and call it phi. It is not particularly difficult to find two line segments with the ratio of 1.6. The measuring place can be arbitrary, and it can be adjusted if necessary to make the measured value closer to φ.
Trying to find phi in the human body will produce similar fallacies. A recent study claimed that the golden ratio exists in different proportions of human skulls. But as Dale Ritter, chief lecturer in human anatomy at Albert Medical College, Brown University, Rhode Island, told Life Science magazine:
"I think the first problem of this paper is that there is almost (maybe not) science in it ... so many bones, so many points of interest on these bones, I think there will be at least some" golden ratio "in other parts of the human skeletal system, which is related to: photo: defining the universe.
Although phi is common in nature, its meaning is exaggerated. Petals usually appear in the form of Fibonacci numbers, such as 5 or 8, and pinecones grow outward in the spiral form of Fibonacci numbers. However, Keith Devlin, a mathematician at Stanford University, told Life Science that there are as many plants that don't follow this rule as those that do.
It is said that seashells such as Nautilus have the potential characteristics of phi. But as Devlin pointed out on his website, "Nautilus's shell does grow in a logarithmic spiral, that is, the spiral rotates at a constant angle along its entire length, making it self-similar everywhere. But this constant angle is not the golden ratio. Unfortunately, I know, but it does exist.
Although phi is indeed an interesting mathematical concept, we humans value what we find in the universe. An advocate may see the golden ratio everywhere through phi colored glasses. However, it is always useful to jump out of a specific perspective and ask whether the world really conforms to our limited understanding of it.
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The following is a useful video to explain the golden ratio mathematically from the critical point. Read more about the myth behind the golden ratio. Look at the Khan Academy's explanation of the golden ratio. 1 Forum Comments Jeanna2019165438+21:231October 25th, many people still think that the golden ratio is all over nature and represents perfect beauty-this is a myth. However, phi is a cool mathematical concept. For example, it is related to Fibonacci series: if the ratio of continuous Fibonacci series is taken, it is closer to phi. And like pi, the golden ratio is unreasonable and will continue! Reply to all 1 starts of the view