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2 results

  • 4 - Beyond Classic Origami

  • from Part I - Geometric Constructions
  • Thomas C. Hull
  • Book:
    Origametry
    Published online:
    06 October 2020
    Print publication:
    08 October 2020, pp 58-72

  • Summary

    In this chapter, geometric construction possibilities that go beyond traditional origami are described.Multifolds, which are origami operations that allow for the simultaneous creation of more than one crease, are the main focus of the chapter.Multifolds provide more algebraic power to origami constructions, and multifold methods of performing angle quintisections and 11-gons are described.Alperin and Lang’s proof that multifold origami can find roots of arbitrary polynomials is given.Origami constructions that include curved creases are also explored, showing that they can allow the construction of some transcendental numbers.

  • 2 - Solving Equations via Folding

  • from Part I - Geometric Constructions
  • Thomas C. Hull
  • Book:
    Origametry
    Published online:
    06 October 2020
    Print publication:
    08 October 2020, pp 31-47

  • Summary

    In this chapter, proofs are given that origami can solve quadratic and cubic equations.For example, when folding a point onto a line the resultingcrease line is tangent to a parabola.Methods used include Lill’s Method for geometrically finding real roots of arbitrary polynomials and Margherita Beloch’s solution to solving cubics from the 1930s.