Logical and Algebraic Views of a Knot Fold of a Regular Heptagon

14 pages•Published: June 19, 2013

Fadoua Ghourabi, Tetsuo Ida and Kazuko Takahashi

Abstract

Making a knot on a rectangular origami or more generally on a tape of a finite length gives rise to a regular polygon. We present an automated algebraic proof that making two knots leads to a regular heptagon. Knot fold is regarded as a double fold operation coupled with Huzita's fold operations. We specify the construction by describing the geometrical constraints on the fold lines to be used for the construction of a knot. The algebraic interpretation of the logical formulas allows us to solve the problem of how to find the fold operations, i.e. to find concrete fold lines. The logical and algebraic framework incorporated in a system called Eos (e-origami system) is used to simulate the knot construction as well as to prove the correctness of the construction based on algebraic proof methods.

Keyphrases: computational origami, geometrical constraint solving, knot fold, theorem proving

In: Laura Kovacs and Temur Kutsia (editors). SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science, vol 15, pages 50-63.

Links:	https://easychair.org/publications/paper/37D3
	https://doi.org/10.29007/v8hh

BibTeX entry

@inproceedings{SCSS2013:Logical_Algebraic_Views_Knot,
  author    = {Fadoua Ghourabi and Tetsuo Ida and Kazuko Takahashi},
  title     = {Logical and Algebraic Views of a Knot Fold of a Regular Heptagon},
  booktitle = {SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science},
  editor    = {Laura Kovacs and Temur Kutsia},
  series    = {EPiC Series in Computing},
  volume    = {15},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/37D3},
  doi       = {10.29007/v8hh},
  pages     = {50-63},
  year      = {2013}}

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