Polynomiography and applications in art, education, and science

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Polynomiography is the art and science of visualizing approximation of the zeros of complex polynomials. Informally speaking, polynomiography allows one to create colorful images of polynomials. These images can subsequently be re-colored in many ways, using one's own creativity and artistry. Polynomiography has tremendous applications in the visual arts, education, and science. The paper describes some of those applications. Artistically, polynomiography can be used to create quite a diverse set of images reminiscent of the intricate patterning of carpets and elegant fabrics, abstract expressionist and minimalist art, and even images that resemble cartoon characters. Educationally, polynomiography can be used to teach mathematical concepts, theorems, and algorithms, e.g., the algebra and geometry of complex numbers, the notions of convergence and continuity, geometric constructs such as Voronoi regions, and modern notions such as fractals. Scientifically, polynomiography provides not only a tool for viewing polynomials, present in virtually every branch of science, but also a tool to discover new theorems.

Original languageEnglish (US)
Pages (from-to)417-430
Number of pages14
JournalComputers and Graphics (Pergamon)
Volume28
Issue number3
DOIs
StatePublished - Jun 1 2004

Fingerprint

Education
Polynomials
Fractals
Algebra
Geometry

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Human-Computer Interaction
  • Computer Graphics and Computer-Aided Design

Keywords

  • Arts and humanities
  • Computer graphics
  • Computers and education
  • Mathematical software
  • Polynomials
  • Roots of nonlinear equations

Cite this

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title = "Polynomiography and applications in art, education, and science",
abstract = "Polynomiography is the art and science of visualizing approximation of the zeros of complex polynomials. Informally speaking, polynomiography allows one to create colorful images of polynomials. These images can subsequently be re-colored in many ways, using one's own creativity and artistry. Polynomiography has tremendous applications in the visual arts, education, and science. The paper describes some of those applications. Artistically, polynomiography can be used to create quite a diverse set of images reminiscent of the intricate patterning of carpets and elegant fabrics, abstract expressionist and minimalist art, and even images that resemble cartoon characters. Educationally, polynomiography can be used to teach mathematical concepts, theorems, and algorithms, e.g., the algebra and geometry of complex numbers, the notions of convergence and continuity, geometric constructs such as Voronoi regions, and modern notions such as fractals. Scientifically, polynomiography provides not only a tool for viewing polynomials, present in virtually every branch of science, but also a tool to discover new theorems.",
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Polynomiography and applications in art, education, and science. / Kalantari, Bahman.

In: Computers and Graphics (Pergamon), Vol. 28, No. 3, 01.06.2004, p. 417-430.

Research output: Contribution to journalArticle

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