Mathematics is the science of abstracting specific problems into spatial forms and quantitative relationships，bet365 champions league is a thinking method that examines and studies objects according to mathematical laws。bet365 champions league is abstract thinking，Belongs to advanced thinking forms。But there are no strict boundaries between forms of thinking，Often interpenetrate each other。The symbols used in thinking activities can be representations in perceptual thinking，That is, the memory element，Including estimates of quantitative and spatial relationships，So bet365 champions league is often permeated in artistic activities。

　　The harmony of quantitative relationships in bet365 champions league

The ancient Greek philosopher Pythagoras and the philosophy of the Pythagoreans are typical representatives of bet365 champions league。They think，"number，It is the cause and root of all things”，“Everything is composed of numbers”。The ontological proposition of the Pythagoreans that “everything is number”，Also used in the analysis of the field of art。They focus on the concept of harmony，And harmony is inseparable from quantitative relationships。Pythagoras discovered the relationship between the pitch of the sound and the length of the vibrating string，Is the earliest scholar to use bet365 champions league to think about music harmony。His disciple Argutas also studied the phenomenon of musical intervals (the distance between sounds in height)。The Pythagoreans opened the prelude to the study of the relationship between mathematics and music in the West。Later，Kepler、Galileo、Euler、Fourier、Thinkers such as Hardy have done special research on this。Mathematical theory has become one of the foundations of Western music thought。

Harmony based on quantitative relationships，Can illustrate the universal application of bet365 champions league in the field of art。This is also true in works of art。The application of perspective method based on mathematical principles in painting，Is an important milestone in the history of Western art development。The Renaissance art master Leonardo da Vinci made a great contribution to the theory of perspective，He said: "Any human exploration activity cannot become science，Unless this activity clears its way through mathematical expression and mathematical proof。”He thinks，The purpose of painting is to reproduce nature，The value of painting lies in accurate reproduction，Therefore painting is a science，Same as other sciences，The basis is mathematics。

The aesthetic evaluation of the body also relies heavily on quantitative description。For example，Big eyes、Slim figure, etc.。Vice versa，Five short stature、Negative aesthetic judgments such as slanted eyes and crooked mouth are also based on quantity、Position and other bet365 champions league relationships。Therefore，Consider the structure and proportion of the body in painting composition。The use of the famous golden ratio in painting and design，Fully proves this point。

In addition to simple physical composition，The design of color and light and shade also reflects bet365 champions league。For example，The degree of warmth and coldness of the color tone、Transition of color or light and dark，There is a proportional relationship。Exceeding a certain proportion is exaggeration，Departing from the reality of art。For example，“Bright eyes and good vision” are certainly a sign of a girl’s cuteness，But there is no need to draw human eyes as bright as searchlights。

Of course，The truth of bet365 champions league is not the same as objective reality。The quantitative relationship of things in paintings and other arts does not have to be exactly the same as real things。The symbolic form used in artistic creation itself contains appropriate flexibility in scale。For example，Painting can certainly reflect the original appearance of beautiful things in reality，But you don’t have to pursue 100% “truth”，Including various quantitative proportional relationships。This is after the advent of photography，The reason why painting (including Western painting that emphasizes perspective) has not been replaced。

Despite this，The truth of bet365 champions league still cannot be separated from reality。Chinese painting is not bound by visual rules (such as perspective principles and color matching)，Leave room for imagination and artistic conception，But it does not deviate too much from the laws of quantitative relationships contained in the shapes of real things。When people appreciate ink landscapes，What flows in my heart is a harmonious melody。

Also，Ancient Chinese architecture pays attention to symmetry、Founder。Among them，Existing aesthetic pursuit，Also uses bet365 champions league。The "dougong" structure is a unique shape of ancient Chinese architecture。Dou and Gong，They are all supporting components in wooden structures in my country，At the intersection of columns and beams。The bow-shaped elbow protruding from the top of the column is called an arch，The square timbers between the arches are called buckets。Dougong load-bearing structure，Can make the eaves extend to a greater extent，Not only beautiful in form，And the symmetrical structure can achieve a balance of forces，Making buildings stable。The use of brackets has made ancient Chinese architectural art famous throughout the ages，It is inseparable from bet365 champions league such as precise mechanical calculations。

　　Quantitative stipulation of bet365 champions league forms

The quantitative stipulations contained in musical harmony，Can become the basis for communication between different art types。In the history of Western aesthetics, there is the proposition that "beauty lies in form"，From a certain perspective，This can be interpreted as "Beauty lies in quantity"。About the similarity between art form and mathematical language form，There have been many studies in the academic community。For example，Huang Qinan thinks，In the exchange of meanings of codes and messages in the language of art and mathematics，Have common characteristics，“Achieved the separation of entity and form。The form extracted in this way can be processed formally"。The form and changes of aesthetic objects have mathematical rules to follow。In the process of art creation and appreciation，Authors or aesthetic subjects often use bet365 champions league consciously or unconsciously，Because the laws of art are inseparable from the laws of quantitative changes in aesthetic objects。

In addition，Of course there is bet365 champions league in the field of literature。For example，Chinese ancient poetry, especially metrical poetry，Each sentence has a fixed number of words。This kind of aesthetic creation and aesthetic appreciation，Of course it is also inseparable from mathematical laws。The 20th century Soviet mathematician Kolmogorov used mathematical methods to study the rhythmic organization of poetry，And created a special discipline - art metrology。In addition，Sculpture、Dance and other artistic fields are obviously inseparable from bet365 champions league。In history，The two artistic fields of music and painting can reflect the obvious relationship between art and bet365 champions league。The quantitative stipulation of art forms is the basis for bet365 champions league to communicate different art types。

From the perspective of bet365 champions league，Music is not just an arrangement of sounds at different heights。The primary element of music—melody，It is also a quantitative relationship。Melody refers to the organization of several musical sounds formed through artistic conception、Rhythmic sequence。This sequence consists of pitches、Duration and volume composition。The melody consists of two elements，That is, the melody line (or pitch line) and rhythm。In a continuous melody progression，Various straight or curved shapes formed due to the direction of pitch，These shapes resemble the stretching or undulation of lines in a painting，So it is called the melody line。The melody line unfolds on the horizontal axis of time，The sounds of different pitches (i.e. melody lines) issued one after another and the length of various musical rhythms、Speed ​​and Slow、When pause and other performance functions are combined，Melody can form the various syntax and structures of music。here，Think of melody as the geometric shape of music。So，Music creation and appreciation also involve elements of bet365 champions league。

Due to the intervention of bet365 champions league，Enables communication channels between different departments in the art field。Someone has adapted music into paintings，It can also bring aesthetic enjoyment to people。Because the two contain similar quantitative changes。

　　Quantitative changes and bet365 champions league education

The law of quantitative change can be applied in art education。For example，In music teaching，Teaching methods are also related to mathematics，This is also in line with the rules of bet365 champions league in art。Some scholars advocate that children’s music education should experience music while “moving” rather than “sitting”。This music teaching method that uses body movement，In fact, it can be reduced to a functional relationship or a spatial quantity relationship in geometry。For example，The pitch corresponds to the direction and position of the gesture in space；Sound intensity corresponds to muscle intensity；The sound value is continuously expressed by actions；Pause is expressed by control (pause)；Counterposition expressed as different actions、Opposition in different directions；Chords are a combination of various gestures；A musical phrase is an action paragraph；The harmonic progression is expressed as a continuous progression combining various gestures；The musical form is expressed as the distribution state of motion in space and time；Wait。This kind of body movement can be completely expressed by three-dimensional coordinates of motion (adding the time dimension)。

In addition，Research shows，Music can enlighten the mind。Among them，Training of bet365 champions league，Or at least the application of mathematical laws，It plays a certain role。bet365 champions league in music education further demonstrates the close connection between bet365 champions league and art。actually，The method of music education is one of the ways of bet365 champions league - the application of geometric spatial thinking。

Art is inseparable from bet365 champions league。The form of art has quantitative attributes，The harmony of art is essentially the harmony of quantitative relationships。Therefore，Art creation and appreciation activities are permeated with bet365 champions league，Communication between different art departments can use bet365 champions league，Artistic educational activities also benefit from bet365 champions league。

　(This article is a phased result of the Jiangsu Province Graduate Research and Practical Innovation Plan Project "bet365 champions league and Science from the Perspective of Perspective" (KYCX22_1522)

(Author’s unit: Academy of Fine bet365 champions league, Nanjing Normal University)