American Journal of Applied Mathematics

| Peer-Reviewed |

Elementary Algebra for Origami: The Trisection Problem Revisited

Received: 08 September 2013    Accepted:     Published: 20 October 2013
Views:       Downloads:

Share This Article

Abstract

This article presents an algebraic background in solving the angle trisection problem using origami-folding. Origami has been originally the art of paper folding, and recently aroused strong interest in a wide discipline of science and technology owing to its deep mathematical implication. Origami is also known to be an efficient tool for solving the trisection problem, one of the three famous problems of ancient Greek mathematics. Emphasis in this article is put on the way how the origami-based construction of the trisection corresponds to obtaining a solution for a cubic equation.

DOI 10.11648/j.ajam.20130104.11
Published in American Journal of Applied Mathematics (Volume 1, Issue 4, October 2013)
Page(s) 39-43
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Origami, Paper Folding, Angle Trisection, Construction Problem

References
[1] K. Kasahara: "Origami Omnibus: Paper-Folding for Everybody" (Japan Publication Inc., 1998)
[2] R. Geretschläger: "Geometric Origami" (Arbelos, UK, 2008).
[3] M. A. Dias, L. H. Dudte, L. Mahadevan and C. D. Santangelo: "Geometric Mechanics of Curved Crease Origami", Phys. Rev. Lett. 109 (2012) 114301.
[4] Z.Y. Wei,Z.V. Guo, L. Dudte, H.Y. Liang, and L. Mahadevan: "Geometric Mechanics of Periodic Pleated Origami", Phys. Rev. Lett. 110 (2013) 215501.
[5] M. Schenk and S. D. Guest: "Geometry of Miura-folded metamaterials", Proc. Natl. Acad. Sci. USA 110 (2013) 3276.
[6] M. S. Strano: "Functional DNA Origami Devices", Science 338 (2012) 890.
[7] J. S. Siegel: "Carbon Origami", Nature 486 (2012) 327.
[8] J. Hoffman: "The origami geometer", Nature 483 (2012) 274.
[9] N. Kaloper: "Origami world", J. High Energ. Phys. 05 (2004) 061.
[10] A. Jones, S. A. Morris and K. R. Pearson, "Abstract Algebra and Famous Impossibilities", (2ed., Springer-Verlag, 1994)
[11] H. Abe: "Possibility of trisection of arbitrary angle by paper folding" in SUGAKU Seminar (in Japanese) (Suken Publishing, Kyoto, 1980).
[12] M. P. Beloch: "Sulmetododelripiegamontodella carte per la risouzionedeiproblemigeometricic", Periodico di MathematicheSerie IV, 16 (1936) 104.
[13] T. Hull: "A note on impossible paper-folding", Am. Math. Month. 103 (1996) 242.
[14] H. Huzita: "Axiomatic development of origami geometry", in Proc. of the 1st Int’l Meeting of Origami Science and Technology (1989) pp.143-158.
[15] R. C. Alperin: "A mathematical theory of origami constructions and numbers", New York J. Math. 6 (2000) pp.119-133.
Author Information
  • Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan

Cite This Article
  • APA Style

    Hiroyuki Shima. (2013). Elementary Algebra for Origami: The Trisection Problem Revisited. American Journal of Applied Mathematics, 1(4), 39-43. https://doi.org/10.11648/j.ajam.20130104.11

    Copy | Download

    ACS Style

    Hiroyuki Shima. Elementary Algebra for Origami: The Trisection Problem Revisited. Am. J. Appl. Math. 2013, 1(4), 39-43. doi: 10.11648/j.ajam.20130104.11

    Copy | Download

    AMA Style

    Hiroyuki Shima. Elementary Algebra for Origami: The Trisection Problem Revisited. Am J Appl Math. 2013;1(4):39-43. doi: 10.11648/j.ajam.20130104.11

    Copy | Download

  • @article{10.11648/j.ajam.20130104.11,
      author = {Hiroyuki Shima},
      title = {Elementary Algebra for Origami: The Trisection Problem Revisited},
      journal = {American Journal of Applied Mathematics},
      volume = {1},
      number = {4},
      pages = {39-43},
      doi = {10.11648/j.ajam.20130104.11},
      url = {https://doi.org/10.11648/j.ajam.20130104.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20130104.11},
      abstract = {This article presents an algebraic background in solving the angle trisection problem using origami-folding. Origami has been originally the art of paper folding, and recently aroused strong interest in a wide discipline of science and technology owing to its deep mathematical implication. Origami is also known to be an efficient tool for solving the trisection problem, one of the three famous problems of ancient Greek mathematics. Emphasis in this article is put on the way how the origami-based construction of the trisection corresponds to obtaining a solution for a cubic equation.},
     year = {2013}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Elementary Algebra for Origami: The Trisection Problem Revisited
    AU  - Hiroyuki Shima
    Y1  - 2013/10/20
    PY  - 2013
    N1  - https://doi.org/10.11648/j.ajam.20130104.11
    DO  - 10.11648/j.ajam.20130104.11
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 39
    EP  - 43
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20130104.11
    AB  - This article presents an algebraic background in solving the angle trisection problem using origami-folding. Origami has been originally the art of paper folding, and recently aroused strong interest in a wide discipline of science and technology owing to its deep mathematical implication. Origami is also known to be an efficient tool for solving the trisection problem, one of the three famous problems of ancient Greek mathematics. Emphasis in this article is put on the way how the origami-based construction of the trisection corresponds to obtaining a solution for a cubic equation.
    VL  - 1
    IS  - 4
    ER  - 

    Copy | Download

  • Sections