Solving Polynomials by Iteration

An Aesthetic Approach
  • Scott Crass
Part of the Mathematics and Visualization book series (MATHVISUAL)


One of the classical problems of mathematics is to solve a polynomial equation. One approach to this is to take account of the fact that polynomials have symmetries that can be realized in geometric spaces. The idea is to solve an equation in an elegant way. During the past eight years I have pursued this goal by developing solutions based on iteration. This involves the repeated application of a process that possesses the very symmetries of the polynomial to be solved. An iterative procedure for solving an equation has two aspects:
  • Geometric: a space where the polynomial’s symmetry can be realized

  • Dynamical: an iterated transformation that respects the symmetry of the equation


Symmetric Group Quadric Surface Geometric Space Numerical Exploration Special Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Crass 1999]
    S. Crass. Solving the sextic by iteration: A study in complex geometry and dynamics. Experiment. Math. 8 (1999) No. 3, 209–240.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [Crass 2001]
    S. Crass, 2001. Solving the quintic by iteration in three dimensions. Experiment. Math. 10 (2001) No. 1, 1–24.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [Nusse and Yorke 1994]
    H. Nusse and J. Yorke. Dynamics: Numerical Explorations Springer-Verlag, 1994. UNIX implementation by E. Kostelich.Google Scholar
  4. [Nusse and Yorke 1998]
    H. Nusse and J. Yorke. Dynamics: Numerical Explorations, 2e Springer-Verlag, 1998. Computer program Dynamics 2 by B. Hunt and E. Kostelich.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Scott Crass
    • 1
  1. 1.California State UniversityLong BeachUSA

Personalised recommendations