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Mathematics and art

2019-03-13 来源: 51due教员组 类别: Paper范文

下面为大家整理一篇优秀的paper代写范文- Mathematics and art,供大家参考学习,这篇论文讨论了数学与艺术。欧洲艺术创作领域公认有两次最大的创新,一次是文艺复兴,另一次是本世纪初兴起的现代艺术。两次大的变革都与几何学的变革有关。前者与三维透视几何有关,后者与N维几何和非欧几何有关。对于数学关系在艺术品中的重要性,向来就被一些美学家和艺术家所肯定,他们认为只要恰到好处地调整好数量比例关系,建筑、雕塑、书法甚至音乐、舞蹈等就能产生最美最和谐的艺术效果,通过我们的视觉就能感受到一种完美。


"Where there is beauty, there is beauty," proclus, the ancient philosopher and mathematician, asserted. Kepler also said: "mathematics is the prototype of the beauty of the world." The artistic pursuit of mathematics has become an important driving force for the development of mathematics, so that the French poet novalli once sang: "pure mathematics is a science, but also an art.

In the field of European art creation, it is acknowledged that there are two biggest innovations, one is the Renaissance, the other is the rise of modern art at the beginning of this century. Both of the great revolutions were related to the revolution in 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 deep mathematical structure hidden behind the mainstream painting art of each era -- geometry. In Picasso's case, non-euclidean geometry; Post-modernism, purism there may be now known as fractal geometry. In fact, the importance of mathematical relations in art has always been affirmed by some aestheticians and artists. Famous ancient Greek mathematician Pythagoras is, the viewpoint of "beauty in harmony" is the "harmony" is very important in a relationship of mathematics, the Pythagorean school called "the most wonderful thing," and they think that as long as the right to adjust quantity proportion relationship, architecture, sculpture, calligraphy and music, dance and so on could produce the most beautiful and the most harmonious artistic effect. We can feel a kind of perfection through our vision. For example, the works of Aphrodite and acropolis contain rich and harmonious mathematical proportion.

The ratio that most makes people feel beautiful and harmonious is the golden ratio -- 0.618.

Many people feel very beautiful things, such as conch, which have a lot of secret, its thread is following the golden section! There are also works of art, a few simple geometric objects, that fascinate us because they also employ mathematical techniques such as the golden section. The golden ratio also affects our aesthetic standards. For example, we all like long legs beauty, that is because her body is in line with the golden ratio, that is, from the top of the head to the navel than the distance from the navel to the heel of the distance, and the ordinary people's legs are often not long enough. If you measure your arm, the distance from the middle finger to the elbow joint when the arm is straight is approximately 0.618 to the distance from the elbow joint to the armpit, then your arm is beautiful.

There are many examples of the application of the golden ratio in painting, among which the most famous and the first one is probably the famous artist Da Vinci. He became a great artist because, above all, he was a great mathematician. He devoted himself to the study of human body structure. He discovered the Numbers and proportions hidden in the human body, and applied these to his works of art, making the figures under his paintbrush lifelike. If you carefully study some of his most famous paintings, the last supper, Mona Lisa, etc., you will be surprised to find that there are many golden sections in them!

Music is the externalization of mind and emotion in sound. Mathematics is the product of highly abstract objective things and logical thinking. So does "amorous" music have anything to do with "cold" mathematics? My answer is yes. There are some similarities between mathematics and music. Before a musician's performance level is judged, it is necessary to confirm a minimum premise: his sound is accurate, and only the pitch does not make him a musician. It would be pointless to judge the work of a historian only by saying that he is not lying.

Mathematics and music are two of the greatest products of the human spirit. They are entirely artificial worlds, resplendently self-sufficient in themselves, the former creating an infinite real world with only ten Arabic numerals and symbols, the latter an infinite world of beauty with only five lines and a few tadpolelike notes.

"Spring night on" and Chopin abortion the song melody is also does not exist in nature, in nature, you will never hear music similar to the artificial, another fascinating, because it is your heart, in mathematics, the n dimensional space, infinite space, such as artificial world, even the "2", "line" and "plane" is the product of the human spirit is the most abstract. Moreover, Chopin paid much attention to the mathematical rules, forms and structures of music score. One expert on Chopin called Chopin's music score "having the mathematical characteristics of the language of music score".

Confucius, the great thinker of our country, once mentioned the six arts of ritual, music, archery, archery, calligraphy and mathematics, among which "music" refers to music and "number" refers to exponential science. In this way, Confucius has put music and mathematics side by side.

In December 1952 at a national symposium on nie er, he works in wuhan, wuhan music director of the institute had read out a compelling paper "on sequence structure of the national anthem", in this paper, the whole based on mathematics, so as to put forward a kind of break through the traditional structural theory point of view, the paper of the novel not only caused a sensation, and stimulate the thinking of music workers, all think between mathematics and music may have a profound inner link.

Literature and mathematics may seem like two separate paths, but in fact, there is a strange identity between them. 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. Mathematics in Chinese poetry

Mathematics into poetry, make people full of interest. Such as "a two three li, smoke village four or five, six or seven towers, eighty or ninety branches of flowers. This poem by shao kang of the song dynasty vividly describes the natural and simple rural scene, just like a quietly elegant ink painting. However, half of it is written with Numbers, and the poetic beauty is implied in the harmony between Numbers.

I've been talking about math and art, and I want to tell you that math is a creative art, because mathematicians create beautiful new concepts, because the way math enthusiasts think about math problems makes them feel good. As a math major, I feel this strongly, and I'm glad I told you so in this paper.


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