Elementary Algebra for Origami: The Trisection Problem Revisited
American Journal of Applied Mathematics
Volume 1, Issue 4, October 2013, Pages: 39-43
Received: Sep. 8, 2013; Published: Oct. 20, 2013
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Author
Hiroyuki Shima, Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan
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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.
Keywords
Origami, Paper Folding, Angle Trisection, Construction Problem
To cite this article
Hiroyuki Shima, Elementary Algebra for Origami: The Trisection Problem Revisited, American Journal of Applied Mathematics. Vol. 1, No. 4, 2013, pp. 39-43. doi: 10.11648/j.ajam.20130104.11
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.
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