Mathematics is the learning that abstracts specific problems into the relationship between space form and quantitative relationship，Mathematics thinking is a way of thinking in accordance with the laws of mathematics and research objects。Mathematics thinking is abstract thinking，belongs to the form of advanced thinking。But there is no strict boundary between the form of thinking，Often penetrates each other。Symbols used by thinking activities can be the appearance in perceptual thinking，That is the memory element，Among them, the estimation of quantitative relationship and space relationship，Therefore, mathematical thinking often penetrates in art activities。

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The philosophy of ancient Greek philosophers Pydagoras and the Pythagoras school is a typical representative of mathematical thinking。They think，"Number，The reason and fundamental reason for everything "，"Everything consists of numbers"。Pythagoras School of "Numbers of Everything" ontology propositions，It is also used in the analysis of the art field。They pay attention to the concept of harmony，and harmony cannot be separated from the quantity relationship。Pythages discovered the relationship between the height of the sound and the long distance of the string of vibration，is the earliest scholar who uses mathematical thinking to think about music harmony.。His disciple Alzus also studied the intervention phenomenon (the distance between the sound and sound at the height)。Pythagoras Bet365 app download school unveiled the prelude to the relationship between Western research and music。Later，Capeler、Galileo、Euler、Fourier、Hardy and other thinkers have done special research on this。Mathematics Theory becomes one of the basis of Western music thought。

Harmony based on quantitative relationship，Can explain the universality of mathematical thinking in the art field。This is also the case in art works。The use of perspective method with the basis of mathematical principles in painting，It is an important milestone in the history of Western art development。The art master of the Renaissance Da Vinci has made a huge contribution to perspective，He said: "Any human exploration can become science，Unless this kind of activity is made through mathematics and has proven to open a road for yourself。"He thinks，The purpose of painting is to reproduce nature，The value of painting is to accurately reproduce，Therefore, painting is a science，Like other sciences，The foundation is mathematics。

The aesthetic evaluation of the body also relies on the quantity description。For example，Big eyes、Slim body, etc.。Vice vice versa，Five short body、Negative aesthetic judgments such as eye oblique mouth crooked mouth are also based on quantity、Location and other mathematical relationships。So，The structure and ratio of the body must be considered in the painting composition。The well -known golden segmentation ratio in painting and design，Fully prove this。

Except for the simple body composition，The design of color and light and dark also reflects mathematical thinking。For example，The degree of warmth of color tone、color system or bright and dark transition，There Bet365 app download is a proportional relationship。More than a certain proportion is exaggeration，Det off from the authenticity of art。For example，"Bright Eyes Good" is of course a cute sign of girls，But there is no need to draw people's eyes as the brightness of the probe lamp。

Of course，The truth and objective and true of art are not the same。The number of things in the arts such as painting does not have to be the same as real things。The symbol form used by art creation contains appropriate elasticity in terms of scale。For example，Painting can reflect the original appearance of the United States in reality，But there is no need to pursue 100 % "real"，Including various quantitative proportion relationships。This is after the appearance of photography technology，Painting (including Western painting that emphasizes perspective method) has not been replaced。

Despite this，The truth of art still cannot be separated from reality。Chinese paintings are not bound by visual laws (such as perspective principles and color matching)，Leave room for imagination and artistic conception，But it did not deviate too much from the laws of quantitative relationships contained in the shape of real things。When people appreciate the ink landscape，The harmonious melody flows in my heart。

Another，Ancient Chinese architecture pays attention to symmetry、Founder。Where，There is existing aesthetic pursuit，Mathematics thinking。"Dou Gong" structure is a unique shape of ancient Chinese buildings。Fighting and Gong，All are supporting components in Chinese wooden structures，At the intersection of the columns and beams。The bow -shaped elbow wood exposed from the top of the pillar is called arch，The square cushion between the arch and the arch is called Bet365 app download the fight。Dou Gong load -bearing structure，It can extend the eaves to a large extent，Not only beautiful forms，and the symmetrical structure can achieve the balance of force，Make the building stable。The use of bucket arch makes ancient Chinese architectural art flow through the ages，Mathematical thinking such as precise mechanical computing is inseparable from precision mechanics computing。

　　The specified quantity of the art form

The specified quantity contained in the harmony of music，It can become the basis for communicating with different types of art。There are "beauty in form" propositions in the history of Western aesthetics，From a certain perspective，This can be interpreted as "Beauty in quantitative relationship"。Sameness of art form and mathematical language form，There have been many studies in the academic community。For example，Huang Qinan thinks，In the exchanges between the code of art and mathematical language，There are common features，"The separation of the entity and the form。This kind of refined form can be formally treated "。The form of aesthetic objects and their changes have mathematical laws to follow。In the process of art creation and appreciation,，Author or aesthetic subject often uses mathematical thinking consciously or unconsciously，Because the law of art is inseparable from the number of changes in the number of aesthetics。

other，Of course, there are mathematical thinking in the field of literature。For example，Chinese ancient poetry, especially Gram Poetry，Each sentence has a fixed number of words。This aesthetic creation and aesthetic appreciation，Of course it is inseparable from the laws of mathematics。The 20th Century Soviet mathematician Kormorov Bet365 app download used mathematical methods to study the rhythm organization method of poetry，and founded a special discipline — artistic measurement。other，Sculpture、Dance and other art fields are obviously inseparable from mathematics thinking。In history，Music and painting two arts areas can reflect the relationship between art and mathematics thinking。The quantity of the art form is the basis for mathematical thinking to communicate different art types。

From the perspective of mathematical thinking，Music is not just the arrangement of different high sound。The primary element of music -melody，It is also a quantitative relationship。Melody refers to the organization formed by some music sounds formed by artistic ideas、Series of Rhythm。This sequence is from sound high、Time value and volume composition。The constituent melody contains two elements，that is the melody line (or sound high line) and rhythm。In the continuous melody，The shape of various linear or curves formed due to the direction of the sound height，These shapes are similar to the stretching or ups and downs of lines in the picture，Therefore, it is called the melody line。The melody line is expanded on the horizontal axis of time，Sounds (ie, melody lines) and the length of the rhythm of various music、Quick slow、Combining performance functions such as stopping，Melody can form all kinds of syntax and structure of music。Here，It can be regarded as the geometric figure of music。So，Music creation and appreciation also has the factors of mathematical thinking。

Due to the intervention of mathematical thinking，Makes communication channels between different departments in the art field。Someone once adapted the music as a painting work，It Bet365 lotto review can also bring people aesthetic enjoyment。Because the two contain similar quantitative changes。

　　Quantity changes and art education

The change of quantity can be used in art education。For example，In music teaching，Teaching methods are also related to mathematics，This is also in line with the laws of mathematics thinking in art。Some scholars advocate that children's music education should be in "motion" instead of experiencing music in "sitting"。This music teaching method that uses physical exercise，In fact, it can be restored into a functional relationship or a geometric space quantity relationship。For example，Sound height corresponding gestures are in the direction and location of space; sound intensity corresponds to muscle strength; continuous representation of sound values;、A opposite of different orientations; chords are a combination of various gestures; music sentences are the action paragraphs; harmonious sounds are continuously performed as a combination of various gestures; wait。This physical exercise can be expressed in three -dimensional coordinates of exercise (adding time dimension)。

other，Research indicates，Music has the effect of inspiring mind。Where，Training for mathematical thinking，or at least the use of mathematical laws，It plays a certain role。Mathematical thinking in music education further shows the close connection between mathematical thinking and art。Actually，The method of music education is one of the ways of mathematical thinking -the use of geometric space thinking。

Art is inseparable from mathematical thinking。The form of art has quantitative attributes，The harmony of art is essentially a harmonious relationship。So，The creation and appreciation of art penetrate mathematical thinking，Communication bet365 live casino games of different art departments can use mathematics thinking，Educational activities of art also benefited from mathematical thinking。

　(this article is the "art and science" (KYCX22_1522) phased results)

(Author Unit: Academy of Fine Arts of Nanjing Normal University)