Roots of any Polynomial with Complex Integer Coefficients using Replacement Sequences, Ruler and Compass

TL;DR

This paper presents a geometric and combinatorial method to find roots of polynomials with complex integer coefficients using simple sequence manipulations, avoiding advanced calculations.

Contribution

It introduces a novel approach that employs replacement sequences, a ruler, and a compass to compute polynomial roots without complex arithmetic.

Findings

Roots can be obtained through sequence manipulation and counting.

The method is implementable with basic geometric tools.

No advanced mathematical operations are required.

Abstract

The roots of any polynomial of degree m with complex integer coefficients can be computed by manipulation of sequences made from distinct symbols and counting the different symbols in the sequences. This method requires only primitive operations like replacement of sequences and counting of symbols. No calculations using advanced operations like multiplication, division, logarithms etc. are needed. The method can be implemented as a geometric construction using only a ruler and a compass.