Geometric solution of a six order equation by three-fold origami

Research Article
Open access

Geometric solution of a six order equation by three-fold origami

Yige Chen 1*
  • 1 The Second High School Attached to Beijing Normal University    
  • *corresponding author 1020050627@qq.com
TNS Vol.5
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-915371-53-9
ISBN (Online): 978-1-915371-54-6

Abstract

Robert J. Lang has proposed a theorem that when solving equations using multi-folds origami, general equations of order n can be solved using n-2 simultaneous folds. However, recently Jorge C. Lucero proved that arbitrary five order equations can be solved using two simultaneous folds. Combining this with the fact that one single fold can solve general quartic equations, the writer questions that whether the theorem may be altered into general equations of order n can be solved by n-3 simultaneous folds. Thus, in this paper, a method of geometric graphing -Lill’s method is used to try to solve six order equations with three simultaneous folds. By conducting case analysis using theoretical knowledge, it can be found that the six order equations can be possibly solved by three simultaneous folds. Besides, a comparison of solving equations with origami constructions and compass-and-straightedge is carried out. The result will encourage more research on using origami to solve higher order equations and inspire people to pay more attention to origami construction, which is more powerful, accurate, and efficient than the compass-and-straightedge people usually use.

Keywords:

origami, analytic geometry, limit, equations, Lill’s method

Chen,Y. (2023). Geometric solution of a six order equation by three-fold origami. Theoretical and Natural Science,5,454-459.
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References

[1]. M. Nadinne. History of Origami, https://plymouthlibrary.org/wp-content/uploads/History-of-Origami.pdf

[2]. Y. Huang, B. Li. Origami and Mathematics, 2012.

[3]. Alperin, R. C., & Lang, R. J. (2009). One-, two-, and multi-fold origami axioms. Origami, 4, 371-393.

[4]. Hull, T. (1996). A note on" impossible" paper folding. American Mathematical Monthly, 103(3), 240-241.

[5]. Lucero, J. C. (2018). Geometric solution of a quintic equation by two-fold origami. arXiv preprint arXiv:1801.07460.

[6]. Bertschinger, T. H., Slote, J., Spencer, O. C., & Vinitsky, S. The Mathematics of Origami.

[7]. Hull, T. C. (2011). Solving cubics with creases: the work of Beloch and Lill. The American Mathematical Monthly, 118(4), 307-315.

[8]. Tabachnikov, S. (2017). Polynomials as polygons. The Mathematical Intelligencer, 39(1), 41-43.

[9]. TivnanR. Lill’s Method. https://www.geogebra.org/m/jreyczgq

[10]. S. Gu. Origami, The Fun of Thinking, 2012.

Cite this article

Chen,Y. (2023). Geometric solution of a six order equation by three-fold origami. Theoretical and Natural Science,5,454-459.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)

ISBN：978-1-915371-53-9(Print) / 978-1-915371-54-6(Online)
Editor：Marwan Omar, Roman Bauer
Conference website: https://www.confciap.org/
Conference date: 25 March 2023
Series: Theoretical and Natural Science
Volume number: Vol.5
ISSN：2753-8818(Print) / 2753-8826(Online)

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References

[1]. M. Nadinne. History of Origami, https://plymouthlibrary.org/wp-content/uploads/History-of-Origami.pdf

[2]. Y. Huang, B. Li. Origami and Mathematics, 2012.

[3]. Alperin, R. C., & Lang, R. J. (2009). One-, two-, and multi-fold origami axioms. Origami, 4, 371-393.

[4]. Hull, T. (1996). A note on" impossible" paper folding. American Mathematical Monthly, 103(3), 240-241.

[5]. Lucero, J. C. (2018). Geometric solution of a quintic equation by two-fold origami. arXiv preprint arXiv:1801.07460.

[6]. Bertschinger, T. H., Slote, J., Spencer, O. C., & Vinitsky, S. The Mathematics of Origami.

[7]. Hull, T. C. (2011). Solving cubics with creases: the work of Beloch and Lill. The American Mathematical Monthly, 118(4), 307-315.

[8]. Tabachnikov, S. (2017). Polynomials as polygons. The Mathematical Intelligencer, 39(1), 41-43.

[9]. TivnanR. Lill’s Method. https://www.geogebra.org/m/jreyczgq

[10]. S. Gu. Origami, The Fun of Thinking, 2012.

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