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Document Type

Article

Abstract

Throughout history, both quadratic and cubic polynomials have been rich sources for the discovery and development of deep mathematical properties, concepts, and algorithms. In this article, we explore both classical and modern findings concerning three key attributes of polynomials: roots, fixed points, and modulus. Not only do these concepts lead to fertile ground for exploring sophisticated mathematics and engaging educational tools, but they also serve as artistic activities. By utilizing innovative practices like polynomiography—visualizations associated with polynomial root finding methods—as well as visualizations based on polynomial modulus properties, we argue that individuals can unlock their creative potential. From crafting captivating fractal and non-fractal images, paintings, posters, sculptures, fashion statements, jewelry designs, to animations, games, dance, poetry, and more, these pursuits appeal to the curiosity of students from middle and high school onwards and to the broader public, including artists. Furthermore, they signify the expansion of art-math activities into the realm of arbitrary degree polynomials, inviting exploration into the fusion of art and mathematics, thereby unveiling a boundless tapestry of possibilities. With the rise of generative A.I., polynomiography potentially finds another vast domain of utilization.

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