Mathematical elucidation of the traditional Japanese fan focusing on its structure

Abstract

Japanese traditional folding fan has the unique 3D expression that does not arise in the other work of art. The painted image on the fan deforms, when it is folded into convex-concave configuration and fixed to the bamboo bones，due to the difference between the shrinking percentage of the outer arc and the inner arc. Many of the fans made until the Edo era are thought to be painted in consideration of the deformation, but it still hasn't been recognized. In this study，we try to have the digital fan model for clarifying the deformation on the fan face due to some parameters such as length of the bones. Further, we try to obtain the original plan view from the images of the folded fan as one of the reverse problems.