Solving Cubic Equations by ORIGAMI

  • Moritsugu Shuichi
    University of Tsukuba Graduate School of Library, Information and Media Studies

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  • 折り紙による3次方程式の解法について
  • オリガミ ニ ヨル 3ジ ホウテイシキ ノ カイホウ ニ ツイテ

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Abstract

We show an algebraic proof of the method for solving cubic equations by ORIGAMI (paper folding). Using ORIGAMI, we can solve the construction problems that are unsolvable in Euclidean geometry, such as angle trisection and doubling cubes. In our formulation, we solve the radical membership problem in polynomial ideals computing a Grobner basis together with constraints of parameters, which correspond to geometrically degenerate cases. Consequently, cubic equations are clearly solved as construction problems. We also show the construction of another solution by trigonometric functions, that is an application of angle trisection by ORIGAMI.

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