# Introduction

**History**

Before using the practical notations which was developed in the 15th century, equations were written in words. For example, an algebra problem from the Chinese Arithmetic in Nine sections, circa 200 B.C.E begins. "Three sheafs of good crop, two sheafs of mediocre crop and one sheaf of bad crop are sold for 29 dou". This statement can be written in the mathematical form,** **

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**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Rene Descartes**

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**Example :** in the quadratic equation

, the letters a, b, and c represent known values (coefficients), while x represents the unknown solution to the equation.

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Polynomiography is defined to be the art and science of visualization in approximation of the zeros of complex polynomials, It is meant to convey the idea that it represents a certain graph of polynomials, but not in the usual way of graphing, say a parabola for a quadratic polynomial.

According to the Fundamental Theorem of Algebra, a polynomial of degree n, with real or complex coefficients, has n zeros (roots) which may or may not be distinct. The task of approximation of the zeros of polynomials is a problem that was known to Sumerians (third millennium B.C.). This problem has been one of the most influential problem in the development of several important areas in mathematics. Polynomiography offers a new approach to solve and view this ancient problem, while making use of new algorithms and today's computer technology. Polynomiography is based on the use of one or an infinite number of iteration functions designed for the purpose of approximation of the roots of polynomials

# The Making of "Mona Lisa in 2001"

A polynomial of degree 10 was used to produce the left polynomiograph Then

as a result of zooming in on one of the significant parts of that image, the right image was obtained. A coloration of various layers resulted in the _final image.

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Â **Polynomiographs leading to " Mona lisa in 2001" **

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**Polynomial**

Polynomials areÂ the sums of monomials

Variable: whose value changes.

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**Example :** *x, y *

Constants: whose values are fixed. Example: 4, 87, etc.,

Consider,

*p(x) = x+6*

Here* x* is a variable and 6 is a constant

In general, the function

*p(x),*

P(x) =

where,** **are real numbers and* n* is a non-negative integer

is polynomial in x over real *, P(x)* is called a polynomial in * x*.

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