Computational origami construction of a regular heptagon with automated proof of its correctness

Authors:
Judit Robu;Tetsuo Ida;Dorin Ţepeneu;Hidekazu Takahashi;Bruno Buchberger
Affiliations:
Babeş-Bolyai University, Cluj-Napoca, Romania;University of Tsukuba, Tsukuba, Japan;University of Tsukuba, Tsukuba, Japan;Yokaichi High School, Shiga, Japan;Research Institute for Symbolic Computation, Johannes Kepler University, Austria
Venue:
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
Year:
2004

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Abstract

Construction of geometrical objects by origami, the Japanese traditional art of paper folding, is enjoyable and intriguing. It attracted the minds of artists, mathematicians and computer scientists for many centuries. Origami will become a more rigorous, effective and enjoyable art if the origami constructions can be visualized on the computer and the correctness of the constructions can be automatically proved by an algorithm. We call the methodology of visualizing and automatically proving origami constructions computational origami. As a non-trivial example, in this paper, we visualize a construction of a regular heptagon by origami and automatically prove the correctness of the construction.