Solving Polynomials by Iteration
An Aesthetic Approach
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
KeywordsSymmetric 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.
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