Asem Kasem
ABSTRACT
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.
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- T. Ida, H. Takahashi, M. Marin, A. Kasem, and F. Ghourabi. Computational Origami System Eos. In Origami<sup>4</sup> Fourth International Meeting of Origami Science, Mathematics and Education. A K Peters Ltd, 2009.Google Scholar
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Index Terms
- Origami axioms and circle extension
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