Formalizing Polygonal Knot Origami
Formalizing Polygonal Knot Origami
复制标题
形式化多边形结折纸
DOI：
10.1016/j.jsc.2014.09.031
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发表时间：
2014
影响因子：
0.7
通讯作者：
Tetsuo Ida and Fadoua Ghourabi and Kazuko Takahashi
中科院分区：
文献类型：
--
作者：
Fujita H;Yagishita N;Aratani S;Nishioka K;Nakajima T;Tetsuo Ida and Fadoua Ghourabi and Kazuko Takahashi
我们展示了计算机辅助折纸法构建正多边形结。该构造是通过基于代数方法的自动证明完成的。给定足够长度的矩形折纸或有限带子，我们可以通过三折构造最简单的结。如果我们在不扭曲胶带的情况下将结紧紧系紧，则结的形状将成为正五边形。我们进一步正式地对结折叠进行分析，以实现自动化构建和验证。特别是，我们展示了正五边形和七边形结的构造和证明。我们使用了一个名为 Eos（电子折纸系统）的软件工具，它结合了 Huzita 基本折叠操作的扩展用于构造，以及 Gröbner 基础计算用于证明。我们的研究得出了关于多边形结的更数学严谨性和更深入的结果。
We present computer-assisted construction of regular polygonal knots by origami. The construction is completed with an automated proof based on algebraic methods. Given a rectangular origami or a finite tape, of an adequate length, we can construct the simplest knot by three folds. The shape of the knot is made to be a regular pentagon if we fasten the knot tightly without distorting the tape. We perform the analysis of the knot fold further formally towards the automated construction and verification. In particular, we show the construction and proof of regular pentagonal and heptagonal knots. We employ a software tool calledEos(e-origami system), which incorporates the extension of Huzita's basic fold operations for construction, and Gröbner basis computation for proving. Our study yields more mathematical rigor and in-depth results about the polygonal knots.