Diagram, Dynamic Geometry and Sangaku

Abstract

We have developed a web-based system of presenting Sangaku. Sangaku is a way of presenting theorems and conjectures in geometry in one sheet of votive picture. Sangaku was used for temples in Japan to exchange geometrical findings, and has been studied as a traditional form of Japanese mathematics called Wasan. We developed a diagrammatic reasoning that directly uses geometric objects as primitives for reasoning, while tools called dynamic geometry software have also been developed. In developing the web-based Sangaku presentation system, we used diagrammatic reasoning which allows users to directly manipulate geometric objects. As a result, geometric findings can be presented not in a static manner of a single picture, but in a dynamic manner of operational geometric objects. Some examples of Sangaku can be seen at: http://www.sys.tutkie.tut.ac.jp/MuJapan.html.