Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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History of solving polynomial equation by paper folding

종이접기를 활용한 방정식 풀이의 역사

  • Received : 2023.02.01
  • Accepted : 2023.02.20
  • Published : 2023.02.28
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Abstract

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

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References

  1. R. ALPERIN, R. LANG, One-, two-, and multi-fold origami axioms, Origami 4 (2009), 371-393. 
  2. R. ALPERIN, A mathematical theory of origami constructions and numbers, New York Journal of Mathematics 6 (2010), 119-133. 
  3. D. AUCKLY, J. CLEVELAND, Totally real origami and impossible paper folding, American Mathematical Monthly 102(3) (1995), 215-226.  https://doi.org/10.1080/00029890.1995.11990562
  4. CHOI Jae-ung, Solving polynomial equations by origami and GeoGebra, Ph. M. Thesis, Kongju National University, 2018. 
  5. CHOI Wonbae, Hilbert and Formalism, The Korean Journal for History of Mathematics 24(4) (2011), 33-43. 
  6. T. CHOW, K. FAN, The Power of Multifolds: Folding the Algebraic Closure of the Rational, Origami 4 (2009), 395-404. 
  7. D. COX, Galois theory. 2nd edition. Pure and Applied Mathematics (Hoboken). John Wiley & Sons, Inc., Hoboken, NJ, 2012. 
  8. E. DEMAINE, J. O'Rourke, Geometric folding algorithms: linkages, origami, polyhedra, Cambridge University Press, 2007. 
  9. M. FRIEDMAN, A History of Folding in Mathematics: Mathematizing the Margins, Birkhauser, 2019. 
  10. F. FROBEL, Gesammelte padagogische Schriften, Enslin, 1874. 
  11. O. HENRICI, On congruent figures, Longman, 1879. 
  12. T. HULL, Solving cubics with creases: the work of Beloch and Lill, The American Mathematical Monthly 118(4) (2011), 307-315.  https://doi.org/10.4169/amer.math.monthly.118.04.307
  13. T. HULL, Project Origami: Activities for Exploring Mathematics, 2nd Edition, A K Peters/CRC Press, 2012 . 
  14. T. HULL, Origametry: Mathematical Methods in Paper Folding, Cambridge University Press, 2020. 
  15. H. HUZITA, La recente concezione matematica dell 'origami-trisezione dell' angolo, Scienza e gioco (1985), 433-441. 
  16. J. JUSTIN, Resolution par le pliage de l'equation du troisieme degre et applications geometriques, L' Ouvert (1986), 9-19. 
  17. J. KONIG, D. NEDRENCO, Septic Equations are Solvable by 2-fold Origami, Forum Geometricorum 15 (2016), 193-205. 
  18. R. LANG, Origami Design Secrets: Mathematical Methods for an Ancient Art, A K Peters, 2003. 
  19. D. LARDNER, A treatise on geometry and its application to the arts, the cabinet cyclopaedia, Longman, 1840. 
  20. E. LILL, Resolution graphique des equations numeriques d'un degre quelconque a une inconnue, Nouvelles Annales de Mathematiques 2(6) (1867), 359-362. 
  21. P. MAGRONE, V. TALAMANCA, Folding cubic roots: Margherita Piazzolla Beloch's contributions to elementary geometric constructions, Proceedings, 16th Conference on Applied Mathematics Aplimat (2017), 971-984. 
  22. Y. NISHIMURA, Solving quintic equations by two-fold origami, Forum Mathematicum 27(3) (2015), 1379-1387.  https://doi.org/10.1515/forum-2012-0123
  23. T. ROW, Geometric Exercises in Paper Folding, Open Court, 1901. 
  24. G. VACCA, Della piegatura della carta applicata alla geometria, Periodico di Mathematiche 4(10) (1930) 43-50. 
  25. YANG Seong-Deog, JO Kyeonghee, On Hilbert's 'Grundlagen der Geometrie', The Korean Journal for History of Mathematics 24(4) (2011), 61-86.