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3/18/2012

江苏大学理学院

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contents

Poetry and fuzzy

Music and Mathematics

Art - the source of mathematical ideas

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1. Poetry and fuzzy Literature and art in some places is difficult to differentiate. Poetry are calculated literature, whether it Can be calculated as art or not? Literature adapted for script can move on stage, to the screen,，Poetry can ， become lyrics, poetry painting, painting match with poems, Literature and art boundary is fuzzy, The language art and literature is sometimes vague, It is not only necessary, but also to use this kind of ambiguity.

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take from “Thinking of My Brothers on a Moonlight Night” of Du Fu 《月夜忆舍弟》 月夜忆舍弟》 Moonlight is not as bright as it was Back in my old home;(露从今夜白，月是故乡明 露从今夜白， 露从今夜白 月是故乡明) Also about white hair verse of Du Fu. I cannot bear to scratch my grizzled hair; It grows too thin to hold a light hairpin. (白头搔更短，浑欲不胜簪 白头搔更短， 白头搔更短 浑欲不胜簪) Express what the poet's a sentiment, feeling. It put this have no so facts to clear. At this point, Just have a branch of mathematics, Fuzzy mathematics likewise. It tried to put some fuzzy object to mathematics description

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Greek philosopher made following the paradox of 'chain of reasoning ' ：" a grain of wheat must not be a heap. For any positive integers n, if n wheat have not piled up, even with n+1 wheat will not constitute a heap. Thus, under the principle of mathematics, barley-corn is not much of a heap. " Zadeh propised the concept that the first collection of ? X A characteristics of the concept of function is to define ：

?1 f A (x ) = ? ?0,

x ∈ A, x ? A,

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江苏大学理学院

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This shows that the use of the functions of the 55 year old man is the possibility of the field size, or degree 0.5, 60 years old, aged 65 years of 0.8.Iit is nearly seventy years old, is over 0.9 0 ． more than 97. for the elderly "set". ,Sixty and sixtyfive years old respectively give to the aforementioned formula.. However, there are two basic problems ： the function to determine subject to the threshold is reasonable. Is it reasonable? In today, the flowers from white last year the red line, "white" and "red" the description of the collection is also vague set. "Red" vague to constitute a set of modern science has as a "red" establish a reasonable degree of dependence and threshold. Modern physic the definition for the visual basic features.

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People no longer than 20 million hair roots or (2 A simple method is feasible，Define “gray” for the membership function： 4

?0 , 当n ≤ 2 × 10 , ? n ? f A (n ) = ? , 当2 × 10 4 < n < 105 , 2 × 10 5 ? , 当n > 105 , ?1 ?

One says a personal gray-haired root number. Give provision a threshold. For example, when the the Just think this person is "gray" weng. When the Just don't call "gray" weng

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2.Music and Mathematics Music and the history of mathematics more long associated. In Pythagoras(毕达哥拉斯)era, music is part of 毕达哥拉斯) 毕达哥拉斯 mathematics. The music to explain the Pythagorean universal harmony of the universe, and this also applies to mathematics. Pythagoras say a father is music theory. He drove ChanXian harmonic music and the relationship between ChanXian chord length.

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Two stretch tight string the equally, if one length is two times longer than another, it caused the harmonics, moreover two sound just right difference octave. If ratios of the two chord length are 3:2, then they have another kind of harmonics, this time the short string sends out the interval long string sends out pitch five degrees. In fact, each kind of harmonics have the positive integer ratio. It was considered as beautiful melody mathematics. However, the ancient Greece philosophers are looked in reverse, they thought this beautiful melody is only one side of the mathematics.

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Euclid once writes the work of music as well, studied the team work of super - diapason and once drew up a scale. Music become an important component in the ancient Greece bright culture is closely together with mathematics to contact . After Middle Ages, arrive Renaissance, cultural spirit of the Greece spread in Europe. European modern times not only the artist, but also numerous scientists and mathematician is caring about music. Daniel Bernoulli obtains one second-order to the stringed musical instrument research in ordinary differential equation in 1732.

d dy α (x ) + y = 0, dx dx

Its solution is a zeroth order Bessel function.

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Daniel Bernoulli and Euler pulls to still make a super - search to various wind instrument, but encounter secondorder partial differential equations and even involved third-order fourth order partial differential equations.

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As a representative in 20th century, Schrodinger is a world-renowned scientist, and a well-accomplished and broad interesting scientist. Who is also king on poetry, drama and language. Learn from the idea of esthetics of science, Pythagorean found a strange relationship between music and sequence. A vibrating string, actually contains the positive integer sequence that Schrodinger sought. Schrodinger’s idea is musical. The vibration of strings, have similar forms of wave equation. A wave equation, just add a certain mathematical conditions, will produce a sequence. According to this opinion, Schrodinger founded an atomic theory, and he got electronic wave equation finally.

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? 2ψ ? 2ψ ? 2ψ 8π 2 m + 2 + 2 + 2 ( E ? V )ψ = 0. 2 ?x ?y ?z h

This is a very wonderful equation. It is the second-order partial differential equation about x , y and z . m says electronic quality,E is total energy, is potential energy,h is V Planck’s constant. In the equationm , E , embodies the V ψ electronic particles sex, embodies the electronic volatility. Visible, this type is the electronic wave unified perfectly.

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In ancient Greece graceful literature, rational philosophy and idealized architecture and sculpture, is reflected in the mathematical influence. All art, including the architecture, sculpture, literature has a concise and simple beauty

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3.Art - the source of mathematical ideas

Greek mathematical shows a static characteristic, corresponding with the constant mathematics. Greek temples gave people a quiet impression -- thought and spirit being in peace condition; the images in the carving are static, giving a person with halcyon feeling; the static feature Greek drama is also obvious. There are few violent action and they pay more attention to the ups and downs of mind just as in the form of refined mathematics there are abundant thoughts. The deduction in Greek mathematics made the ancient Greeks hold the logos in esteem reaching the degree of extremely. In their emotional experience, they do their utmost to search logos. They praise the hero because not only their brave but also that the action of the heroes are in accordance with the logos. In Greek’s mind, deductive reasoning is full of logic, consistency, integrity, so it is indisputably a kind of art.

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The dot, line, side, number appearing in Greek mathematical all already showed a degree of abstraction, and it is idealistic to the reality. Such kind of preference for abstraction and idealization also left a deep imprint in its culture. Their sculptures don't emphasize individual man or woman, but pay attention to the ideal mode. This kind of pursuit for idealization and abstract sculptures led to the pursuit standardization of the percentage of each part (including every part of human body). The Greeks not only gives the gold standard 0.618, but also not ignore the proportion of toes or fingers. The architecture of ancient Greek is also standardized. In simple and plain buildings, length, width and high follow a certain proportion. They combined the insisting of the ideal proportion and insisting of abstract form closely. Art is the unity of ideal and abstract, and mathematics is also the unity of ideal and abstract.

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The characteristic of leakproofness of mathematics causality is also being profoundly embodied in Greek drama. Greek tragedies emphasize the of destiny and the role of inevitability. The rationality of the effect of fate and the application of deductive inference is consistent in essence and congenital. Mathematical knowledge is eternal, and the mathematical knowledge about the universe is elective forever. By the dominance of this thought, Greek art tries hard to reflect and depict not the individuals but the extensive and basic characteristics of the entire human.

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Leonardo Da Vinci established a new mathematical perspective theory system, put this mathematical spirit in perspective theory system into art of painting and created a 3/18/2012 23 江苏大学理学院 brand new painting style.

Construction, decoration and geometry of relationship are more direct. Although ancient haven't Group Theory, Symmetry and symmetry patterns have scattered among the decorative arts of many peoples. Spain's Alhambra Palace, the decorating has appeared in 17 symmetrical patterns. One of modern art theorists Kandinsky think a great, almost limitless freedom is characteristic of modern art; As a modern mathematics foundation set theory, the founder of cantor thinks that freedom is the essence of mathematics. Kandinsky "structure" introduce painting, this again and famous contemporary mathematics genre Boolean ba base "structuralism" by chance. In 1923 Kandinsky public at “point line face” of book, mathematics and the arts directly linked, book of the geometric basic object in the art performance makes a thorough analysis.

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Construction, decoration and geometry of relationship are more direct. Although ancient haven't Group Theory, Symmetry and symmetry patterns have scattered among the decorative arts of many peoples. Spain's Alhambra Palace, the decorating has appeared in 17 symmetrical patterns. One of modern art theorists kandinsky think a great, almost limitless freedom is characteristic of modern art; As a modern mathematics foundation set theory, the founder of cantor thinks that freedom is the essence of mathematics. Kandinsky "structure" introduce painting, this again and famous contemporary mathematics genre Boolean ba base "structuralism" by chance. In 1923 Kandinsky publicat “point line face” of book, mathematics and the arts directly linked, book of the geometric basic object in the art performance makes a thorough analysis.

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In mathematics and the arts, and the relationship of the problems involved in art mainly are: the spirit and thoughts have math? In mathematics, also have the spirit of art and thought of influence exist? The second is inevitable question is: Mathematicians to look at it the relationship between mathematics and the arts? Artist and how to treat the art and mathematical relationship? Chess, including go, Chinese chess, etc. Chess activity to some extent can also see it as a mathematical activities. It is also a kind of art and mathematical rendezvous. American mathematician A ? Bulkier said: "I have already mentioned the mathematics as a art concept, namely concepts constitute the idea of poetic. This as starting point can assert that can appreciate mathematics, need for a very special thinking in the world of various concept in the spiritual jas and beauty have a unique sensibility. The mathematician rarely have the capability, this is not sufficient strange..." However, and artistic similarity is clear: to appreciate music or painting, it must have some sort of education, that is, must learn to some kind of language." 3/18/2012 26 江苏大学理学院 "Our poem" is written by "mathematical language."

Mathematics is the creative art, because mathematician create a better concepts; Mathematics is the creative art, as well as artists because mathematicians to work life, as well as, thinking; Mathematics is the creative art, because mathematician so treat it. American mathematician, mathematics historian M ? Klein make another describe: "music can inspire and soothing feelings, painting what is pleasing, philosophy get wisdom, technology can improve material life, but the math they provide above all.

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