Mathematical Form

M.C. Escher is a great modern Dutch printer, and his works are outstanding for their artistic combination of ration and imagination and of science and art, which is closely related to his study on mathematical methods, especially the principles of symmetry in geometry. Based on raw materials, this thesis begins with Escher's exploration of mathematical methods, analyzes his regular division of the plane with preliminary symmetric principles-concepts about symmetry and isometry (transformation, rotation, reflection and glide-reflection) in geometry, and discusses the inspiration of Escher's works, the rational and sentimental factors in the process of artistic design, artistic design and experiment, the relationship between artistic design and science.