正４面体と正６面体との共通の展開図の構成に関する研究

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Other Title
  • Construction of Common Unfolding of a Regular Tetrahedron and a Cube

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Description

本稿では，正 4 面体と立方体の共通の展開図を生成する手続きを与える．これは生成する辺の長さを調整可能である．正 4 面体の辺の長さに誤差を許せば，この手続きは停止して，立方体とほぼ正 4 面体の共通の展開図を生成する．誤差を許さない場合は，この手続きは停止せず，無限個の点の集合として，立方体と正 4 面体の共通の展開図が得られると予想している．またこの手続きは，適切な連分数展開表現を持つ実数を与えれば，フラクタルパターンの自動生成を行うこともできる．A procedure that produces a common unfolding of a regular tetrahedron and a cube is given. It is adaptable to the length of an edge. If we allow a small error of the length of an edge of the tetrahedron, the procedure certainly halts and generates a common unfolding of a cube and an almost regular tetramonohedron. If we wish to generate the common unfolding of them with accuracy, we conjecture that the procedure does not halt and we obtain the common unfolding in the limit as a set of infinitely many points. The procedure has a potential to design a fractal structure given in a continued fraction form.

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Details 詳細情報について

  • CRID
    1574231876753633152
  • NII Article ID
    110008583108
  • NII Book ID
    AN1009593X
  • Text Lang
    en
  • Data Source
    • CiNii Articles

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