Computational origami of a morley’s triangle

Authors:
Tetsuo Ida;Hidekazu Takahashi;Mircea Marin
Affiliations:
Department of Computer Science, University of Tsukuba, Tsukuba, Japan;Department of Computer Science, University of Tsukuba, Tsukuba, Japan;Department of Computer Science, University of Tsukuba, Tsukuba, Japan
Venue:
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Year:
2005

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Abstract

We present a computational origami construction of Morley’s triangles and automated proof of correctness of the generalized Morley’s theorem in a streamlined process of solving-computing-proving. The whole process is realized by a computational origami system being developed by us. During the computational origami construction, geometric constraints in symbolic and numeric representation are generated and accumulated. Those constraints are then transformed into algebraic relations, which in turn are used to prove the correctness of the construction. The automated proof required non-trivial amount of computer resources, and shows the necessity of networked services of mathematical software. This example is considered to be a case study for innovative mathematical knowledge management.