The ancient Greeks attached great importance to the relationship between artistic form and mathematical proportion. After studying various formal laws, they established the golden ratio of 5∶8, and designed and created sculptures and buildings according to this ratio. Perikles, a sculptor in the heyday of ancient Greek art, also likes to study figure sculpture with the proportional relationship of numbers. He determined that the proportional relationship between human head and body is 1∶7. His views gradually developed into the later scale standards of 1: 8 and 1: 9.
During the Italian Renaissance, a new generation of Europeans combined painting with geometric knowledge, and the most prominent performance was the application of geometric perspective in painting. Pierrot de la Francesco, a French painter, first mentioned in Perspective of Painting: "In order to make the picture look more natural, the key is to make it conform to human visual laws. Therefore, the human eye is the core of the whole work. If the oil painting is a sketch of the scenery outside the window, then there is only one point in the space, from which the correct visual effect can be obtained. The observer's eyes must be on the same horizontal line as the horizontal line of the oil painting, and focus on the vanishing point of the oil painting. According to the distance between objects, it is helpful to reduce the intersection between the cutting line of perspective and the horizontal line of oil painting. This point is usually outside the picture, and the distance between this point and the vanishing point is the best distance between the viewer and the picture. " This theory soon influenced many artists in the European Renaissance. For example, Michelangelo's Painting on the Ceiling of the Sistine Chapel is a perspective painting. In The Last Judgment, he deliberately made the upper part larger than the lower part, so that every part of the picture seen by the audience on the ground is the same size.
With the continuous development of painting art, Cezanne, known as "the father of modern painting in the 20th century in the West", famously said: "Everything in nature can be represented by spheres, cones and cylinders, that is, according to the perspective law, an object block is focused on the central focus. This means that the horizontal parallel line of width is a division of nature, and it can also be said that it was developed by Almighty and Eternal God, while the vertical line crossing the horizontal line will increase the depth. " Cezanne's theory has had a far-reaching impact on western painting and even contemporary painting throughout the twentieth century.
If the above painters' understanding of mathematics can make people more truly express the image of three-dimensional space on the surface of two-dimensional space, then the non-Euclidean geometry and multi-dimensional space in the 20th century directly led to the emergence of abstract art, cubism and futurism. For example, mondriaan, the representative painter of geometric abstraction, thinks that only abstract geometric figure forms are the most essential of painting. As soon as people see those thick black horizontal and vertical lines, forming squares and rectangles with different sizes of red, yellow, blue and gray, they know that they are their works. Picasso and Braque, the representatives of cubism, are also most concerned about geometric expression, and Braque is the first person to really use the geometric term "cubism" as the name of the painting school. 19 16, Einstein published the general theory of relativity, and time and motion became the focus of artists' attention. The futurist painter Duchamp expressed his interest in how to show the continuous movement process on a still picture in his work Naked Woman Down the stairs No.2, trying to show the fourth dimension of time and space on a two-dimensional picture. Aysil, the most famous printmaker in the Netherlands, used some basic patterns in his plane mosaic, and applied geometric methods such as reflection, sliding reflection, translation and rotation to obtain more patterns.
It can be seen that the influence of mathematics on art has a long history and far-reaching significance.