Synthetic Learning in Art and Mathematics Using a Computer

－Escher's Motif and Plane Tiling－

Abstract

Everyone knows the beautiful tilings by M.C.Escher, one of the most eminent lithographer in the 20th century. His “Heaven and Hell”, based on the geometry of the hyperbolic plane, is the most famous, but shortly before that, Escher conducted a unique research into the patterns on the more familiar Euclidean plane. In this article, we will describe some learning activities, both for synthetic learning and liberal arts education, where students can learn from generating by a computer various patterns and investigating them. Engaged in this activity, they can learn the beauty of art and, at the same time, the usefulness of modern mathematics. Computers will play an indispensable role for the understanding of the structure and experiment in this cross-disciplinary project.