A complex octagon is represented as a group of all polynomials with negative discriminants and at least one real root. Elliptic functions and hypergeometric functions are used to transform polynomials with positive discriminants into the complex octagon. The properties of the complex octagon for several discriminants are presented and indicate it is a precise and well-defined representation of real roots of any polynomial. Simplified methods of finding these roots using modular functions are described.
Perrin Sequences My Chalkboard 