-(UK) james jones
It is said that it meets the following conditions, that is, it belongs to the most perfect female standard body shape:
It is not difficult to see that except for the last one, the rest are related to numbers or mathematics. But I don't have any research on human aesthetics, and I don't know how correct it is.
Similarly, in Mario Livio's book Mathematical Meditation: Evolution of Ancient and Modern Mathematical Thoughts,
I don't have any research on music, but I am surprised that the author's accurate conclusion coincides with the existing state and laws of natural things, which really makes people feel that it is beyond the reach of human beings!
I marvel at such a wonderful and mysterious world, and feel sorry for my almost lack of mathematical knowledge, because I gradually feel that mathematics is the combination of freedom and beauty, and it is the knowledge to enjoy harmony and beauty freely. Therefore, I think most mathematicians must be extremely happy. In a harmonious and beautiful world, what can a person ask for?
But, as the author of this book mentioned, is God a mathematician? Is mathematics a human invention or discovery? However, I prefer this conclusion-"Mathematics is a combination of invention and discovery". For example, Kepler discovered three laws of planetary motion (orbit law, area law and period law respectively), and Newton discovered three basic laws of object motion, and most of them were expressed by almost perfect mathematical propaganda, thus becoming a standard-setting person for the universe.
It can be said that these laws in the universe are a kind of transcendental laws or connections that still exist. These great mathematicians and physicists have just discovered this law, but because of their great creation, that is, invention, they can only be expressed by a nearly perfect mathematical formula.
However, some people hold the opposite view that law is an invention and expression is discovery. But it seems difficult to convince me, and it is estimated that it is difficult to convince the public. But the expression of this law and relation may be just one of the forms invented by human beings, such as "2+2=4" and "2×2=4". These two expressions, the same number, have reached the same conclusion after different forms of operation. It can be seen that there is one such thing in the world, and there is no second or even more such thing.
It is worth noting that in many cases, mathematics has its unique advantages in explaining things. Wegner called it "the effectiveness of mathematics without reason" and successfully explained the world around us. For example, this book mentions an example of such a dialogue:
Although it is a bit close to sophistry, it is indeed the simplest and most effective explanation I have ever heard. In addition, there are some Euclidean geometric theorems that have always been considered self-evident, the double helix structure of deoxyribonucleic acid (DNA) and the transcription of its genetic information, which are used to present the normal frequency distribution curve of data such as height and weight, as well as the application and dependence of statistics and probability in the so-called big data era or digital survival era. ...
This is probably not only because mathematics is the only bridge that can be built quickly between different languages, but also because mathematics has become or has always been a part of our existence, even a part leading to freedom.
First of all, because mathematics is connected with human thinking, it realizes the freedom in the field of thinking, unlike many other aspects of learning, which are more or less restricted by thinking patterns or taboos. Of course, some people think that mathematics is the product of logical thinking. Whoever comes first can at least conclude that mathematical thinking is free.
Secondly, the study of mathematics is always based on natural harmony from the initial phenomenon to the conclusion, and it is a subject to study the free universe. For example, from rational numbers to calculus, from Pythagoras' quaternion to Einstein's law of mutual change of mass and energy, from particle microstructure to the operation law of the universe and so on.
Third, sometimes the conclusion is free or open because the process is free. For example, according to the statistics of different purposes, such as the famous catenary problem, such as multi-dimensional surface and knot problem.
Finally, mathematics is the most convenient and free tool to explain the world. At least at present, there is no more concise and intuitive explanation of cosmic phenomena and laws than mathematics, so the use of this tool is of course the most unrestricted, just as the more self-disciplined people are, the more free they are.
Mathematics studies nature and harmony, while mathematics itself is free and beautiful. This beauty and freedom are not only reflected in the research object, the research process, but also in the research conclusion. I think the following statement about the golden ratio can best reflect this perfect combination of freedom and beauty.
0.6 18 is an auspicious number and an interesting one. In the famous Fibonacci series, the ratio of any two adjacent numbers, the larger the number, the closer it is to this ratio.
Whether it is painting, sculpture, music and other artistic fields, or in architecture, engineering design and other aspects, there is a shadow of the golden ratio everywhere. From the pyramids of ancient Egypt, Notre Dame de Paris and Eiffel Tower to the five-pointed star on the national flag, the arrangement of veins and the crystal structure of molecules.
It is said that many of Leonardo da Vinci's famous oil paintings are laid out in this proportion. It must be said that it is precisely because human beings have mastered the characteristics of natural beauty and the source of artificial beauty that it is a kind of free creation and a kind of free enjoyment to add beautiful things in a harmonious form in the free universe and find beautiful feelings.
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