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2 results

  • 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.

  • CONSTRUCTIONS BY RULER AND COMPASS, TOGETHER WITH A FIXED CONIC

  • Part of
  • SEUNGJIN BAEK, INSONG CHOE, YOONHO JUNG, DONGWOOK LEE, JUNGGYO SEO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 88 / Issue 3 / December 2013
    Published online by Cambridge University Press:
    08 March 2013, pp. 473-478
    Print publication:
    December 2013
    • Article
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  • It is well known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from ancient times that these constructions can be performed when the use of several conic curves is allowed. In this paper, we prove that any point constructible from conics can be constructed using a ruler and a compass, together with a single fixed nondegenerate conic different from a circle.