Origami axioms and circle extension
Origami axioms and circle extension
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DOI：
10.1145/1982185.1982429
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发表时间：
2011-03
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影响因子：
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通讯作者：
Asem Kasem;Fadoua Ghourabi;T. Ida
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文献类型：
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作者：
Asem Kasem;Fadoua Ghourabi;T. Ida
折纸，即折纸，是一种强大的工具，几何结构。1989年，Humiaki Huzita基于对齐一个或多个点和线的组合引入了六种折叠操作[6]。雅克·贾斯廷在他的论文中也提出了七种不同的操作[9]。他的清单包括，没有文字描述，一个额外的操作没有在胡齐塔的论文。贾斯汀的作品是用法语写的，不知何故在研究人员中不为人知。这使得Hatori [5]在2001年“发现”了同样的第七次手术。Alperin和Lang在2006年[1]通过对所涉及的点和线的叠加组合的穷举，证明了这七种操作是对齐的完全组合。胡齐塔没有把他的操作列表称为公理。然而，多年来，术语Huzita公理，或Huzita-Justin或Huzita-Hatori公理，已被广泛用于折纸社区。从逻辑的观点来看，把胡齐塔关于折叠运算的原始陈述称为公理是不准确的，因为它们在平面欧氏几何中并不总是正确的。在本文中，我们提出了精确的声明的折叠操作，命名它们的“公理”是逻辑上有效的，我们做了一些笔记的工作Huzita和贾斯汀。
Origami, i.e. paper folding, is a powerful tool for geometrical constructions. In 1989, Humiaki Huzita introduced six folding operations based on aligning one or more combinations of points and lines [6]. Jacques Justin, in his paper of the same proceedings, also presented a list of seven distinct operations [9]. His list included, without literal description, one extra operation not in Huzita's paper. Justin's work was written in French, and was somehow unknown among researchers. This led Hatori [5] to 'discover' the same seventh operation in 2001. Alperin and Lang in 2006 [1] showed, by exhaustive enumeration of combinations of superpositions of points and lines involved, that the seven operations are complete combinations of the alignments. Huzita did not call his list of operations axioms. However, over years, the term Huzita axioms, or Huzita-Justin or Huzita-Hatori axioms, has been widely used in origami community. From logical point of view, it is not accurate to call Huzita's original statements of folding operations as axioms, because they are not always true in plane Euclidean geometry. In this paper, we present precise statements of the folding operations, by which naming them 'axioms' is logically valid, and we make some notes about the work of Huzita and Justin.