Geometrical Approaches To Visual Art

Both of visual art and geometry, their common ground is based on the expression and recreation of the real universe, however, such an expression and recreation looks very perceptual to visual art, but full of rationality to geometry. Although such the subjects which belonged to science and art individually make a great difference in one's subjective perception, but in actual fact, no matter how variable of its forms, visual art can always reflect the corresponding geometrical ideas of the corresponding times when we looking back to the developing history of visual art. Thus the research is to elaborate the geometrical ideas behind the visual art of each historical stage, and reveal the hidden rational ideas and structures of the perceptual art. Concretely in the research ways, this paper mainly adopt the method of geometry and rational analysis to analyze a series representative visual art forms and works one by one with the basic geometrical principals from the classical Euclidean geometry to the later projective geometry, non-Euclidean geometry, higher dimensional geometry, topological geometry and fractal geometry. In particular, this paper makes a detailed research and analysis to certain art works of their corresponding ideas in the seventeen kinds of plane symmetrical groups, the curved surface and higher dimensional characteristics of non-Euclidean space and the self-similarity of fractal geometry. The preliminary search reveals that no matter what the visual art form is, their hidden geometrical ideas were always people's understandings to the space in the certain scientific circumstances. Thus we can even to say, what kinds of geometry we have, and what kinds of visual art expressing form exists. The recreation of visual art couldn't do without such the manifestation approaches like plane or space; therefore, we would necessarily carry our ideas of time and space in the visual art practice.