Knot Fold of Regular Polygons: Computer-Assisted Construction and Verification

Abstract

We present computer-assisted construction of regular polygons by knot paper fold. The construction is completed with an automated proof based on algebraic methods. Given a rectangular origami or a finite tape, both of an adequate length, we can construct the simplest knot by making three folds. The shape of the knot is made to be a regular pentagon if we fasten the tape tightly without destroying the tape. We performed the analysis of the knot fold further formally towards the computer assisted construction and verification. Our study yielded more rigor and in-depth results about the subject.