A paper on the relationship between mathematics and art

Abstract: Mathematics itself is an art, and the beauty of art cannot be separated from mathematics. Studying the artistic value of mathematics is conducive to promoting the understanding and dissemination of mathematics, promoting artistic creativity and imagination, and cultivating scientific aesthetics and values.

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Keywords: the artistic value of mathematics

Proch Ras, an ancient philosopher and mathematician, asserted: "Where there are numbers, there is beauty." Kepler also said: "Mathematics is the prototype of beauty in this world". The artistic pursuit of mathematics has become an important driving force for the development of mathematics. There seems to be no necessary connection between mathematics and art, however, both mathematics and art are beautiful and internally related. Because almost all human disciplines use mathematics more or less, and art is no exception. In fact, mathematics is not only a science, but also an art itself, and the beauty of harmony and simplicity displayed by mathematics has influenced many art schools.

I. Mathematics and painting

It is recognized that there are two greatest innovations in the field of European artistic creation, one is the Renaissance, and the other is the modern art that rose at the beginning of this century. These two changes are related to the change of geometry. The former is related to three-dimensional perspective geometry, while the latter is related to n-dimensional geometry and non-Euclidean geometry.

There is a profound mathematical structure behind the mainstream painting art of each era-geometry, which in Leonardo da Vinci's view is projective geometry that emphasizes perspective; In Picasso's view, it is non-Euclidean geometry; In postmodernism and purism, now it may be fractal geometry. In fact, the importance of mathematical relations in works of art has always been affirmed by some aesthetes and artists. Pythagoras, a famous mathematician in ancient Greece, put forward the view that "beauty lies in harmony", and one of the most important mathematical relations was called "the most wonderful thing" by Pythagoras school, so they thought that architecture, sculpture, calligraphy and even music and dance could produce the most beautiful and harmonious artistic effect as long as the proportion of quantity was properly adjusted. We can feel a kind of perfection through vision. For example, Aphrodite of Milos and Acropolis of Athens all contain rich and harmonious mathematical proportional relations.

The most beautiful and harmonious ratio is the golden ratio-0.618. Many beautiful things, such as conch, have many secrets, and its line follows the golden section! There are also some works of art and some simple geometric figures, but we are fascinated by them because it also uses mathematical techniques such as the golden section.

There are many examples of applying the golden ratio to painting, among which the most famous and the first one may be the famous artist Da? 9? 9 Finch. He became a great artist because he was a great mathematician first. He devoted himself to the study of human body structure. He discovered the numbers and proportions hidden in the human body, and applied them to his works of art, making the characters in his works vivid and never tired of seeing them. If you carefully study some of his most famous paintings, such as The Last Supper and Mona Lisa, you will be surprised to find that there are too many golden sections!

Second, math and music.

Music is the externalization of mind and emotion in sound, and mathematics is the product of highly abstract and logical thinking about objective things. So, does "sentimental" music have anything to do with "cold" math? My answer is yes. There are some similarities between mathematics and music. Before judging a musician's performance level, we must first confirm a minimum premise: his intonation is accurate, and pure intonation cannot make him a musician. Just like judging a historian's works, it is irrelevant to say that he is not lying.

Mathematics and music are two products of human spirit. They are two brilliant and self-sufficient worlds that are completely artificial. The former created an infinite real world with only ten Arabic numerals and a few symbols, while the latter created an infinite beautiful world with only five lines and some tadpole-shaped notes.

The melodies of "Moonlit Night on a Spring River" and Chopin's "Abortion Song" also do not exist in nature. In nature, you will never hear artificial and charming music, because that is your voice. In mathematics, artificial worlds such as N-dimensional space and infinite space, even "2", "straight line" and "plane" are the most abstract products of human spirit. In addition, Chopin paid great attention to the mathematical rules, forms and structures of music scores. An expert on Chopin said that Chopin's music score "has the mathematical characteristics of music score language".

Confucius, a great thinker in our country, once mentioned the six arts "Rite, Music, Shooting, Imperial, Calligraphy and Numbering", in which "Music" refers to music and "Numbering" refers to mathematics. In this way, Confucius put music and mathematics together.

1952 At the National Symposium on the Works of Nie Er and Xian Xinghai held in Wuhan in February, the president of Wuhan Conservatory of Music read out a striking paper, The Structure of the March of the Volunteer Series, which was based on mathematics, and thus put forward the viewpoint of breaking through the traditional structure theory. The novelty of the paper not only caused a sensation, but also caused the musicians to think. Everyone thinks that there may be a deep internal connection between mathematics and music.

Third, mathematics and literature.

Literature and mathematics seem to be two cars running on different roads, but in fact mathematics and literature have wonderful identity. Literature conveys the results of human rational thinking in the form of sensory experience, while mathematics describes human sensory experience in the form of rational thinking. Literature reveals truth with beauty, while mathematics reveals beauty with truth. Although the direction is different, the essence is unified, mainly in the unity of symbols.

Mathematics into poetry is full of interest. For example, "when you walk to the second or third mile, there are four or five smoke villages, six or seven towers and eighty or ninety flowers." This poem by Shao Kang, a poet in the Song Dynasty, vividly depicts the natural and simple pastoral scenery, just like a beautiful ink painting, but half of it is written in numbers, and the harmony of numbers implies poetic beauty. The following are famous Tang poems from one to ten, which are quite charming:

A piece of ice heart is in the jade pot (Wang Changling), and the second minister helps the old minister (Du Fu).

The Yinshan Mountain shook ten thousand people to cry out (Cen Can), a spell was on the banquet, and the stars were getting thinner (Li Shun).

Cross the fog and forget the words? (Wen) For six years, I sighed for them and sang about facing the west (Han Yu).

On the seventh day of July, the Palace of Eternal Life (Bai Juyi), the Eight Majesties visited 80,000 Aliri (Li Shangyin).

Who saved the admonition book nine times (Li Shangyin), and only carried a few camels with ten drums (Han Yu).

China culture has a long history and profound accumulation. The ancient sages left us a rich cultural heritage. There are many famous sentences in poems, words, songs, poems, legends, novels and essays. It is worth noting that numbers are often embedded in them. Numbers in poetry are like finishing touches, like shining stars in the night sky.

Four. Concluding remarks

Professor Zhang Jiping said: Beauty is the pursuit of human nature and a great driving force for human progress. Art is the expression of beauty, mathematics is the language of beauty, mathematics pursues beauty and creates beauty. The combination of mathematics and art makes beauty more concise. In our life, there is an artistic atmosphere everywhere, and there is also the charm of mathematics. Perhaps, once we thought mathematics was boring. But now, we have to change our past views. Mathematics is an art and an indispensable art in life.