Origami and Geometric Constructions

series-step instructions for origami, folding each action is defined with precision … The purpose of origami geometric constructions is to define one or more points ….

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Origami and Geometric Constructions
Table of Contents

  • Introduction….2
  • Preliminaries and Definitions …2
  • Binary Divisions …4
  • Binary Folding Algorithm….5
  • Binary Approximations…9
  • Rational Fractions…11
  • Crossing Diagonals…12
  • Fujimoto’s Construction…15
  • Noma’s Method …18
  • Haga’s Construction …20
  • Irrational Proportions ….22
  • Continued Fractions …22
  • Quadratic Surds…26
  • Angle Divisions …31
  • Axiomatic Origami…37
  • Preliminaries…39
  • Folding…41
  • Alignments…41
  • Bringing a point to a point P ↔ P …42
  • Bringing a point onto a line (P ↔ L)…42
  • Bringing one line to another line ( L ↔ L) …42
  • Alignments by folding…43
  • Multiple Alignments …44
  • Constructability…44
  • Axiom 6 and Cubic Curves ….45
  • Approximation by Computer…49
  • References…53
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