Steiner chainと和算の環円問題再考 (The study of the history of mathematics 2016)

Abstract

In Wasan which is old mathematics in Japan, Steiner chain was studied by Ajima Naonobu (1732-1798) earlier than Jakob Steiner (1796-1863). Geometry was the major areas of Wasan. Now in practice, it takes a lot of time to solve beautiful geometry problems in the time of the method, but it is difficult to explain them using sophisticated way. If we can show the relevance among the problems clearly in a simple way, we can show more charm of Wasan. This paper will be such an experimental approach. The second purpose of this paper is related to the fact that one of the invariant holds on Steiner chain problems in Japan. This fact is known among people who are interested to solve Wasan geometry problems. Probably for the first time, it was submitted collectively in Tatsuhiko Kobayashi's paper. Although it has passed more than 30 years from that pointing out, the elucidation of it has not been made. We already made another simple proof to Ikeda's theorem and Kenmochi's theorem, using the inversion method. Now, the idea of proof and the other one have been found to be effective to clarify that. This paper will be an effort to answer the problem.