Animation of mathematical concepts using polynomiography

Bahman Kalantari, Iraj Kalantari, Fedor Andreev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

In this paper we demonstrate how a medium called polynomiography, which consists of techniques for visualization of polynomial equations, can be used to animate mathematical concepts, thereby offering a valuable tool for education. More specifically, we will show how it can be used to visualize the following topics: Voronoi regions of points in the plane; multiplication of complex numbers and their interpretation as rotation; sensitivity of polynomial roots as coefficients change; visualization of classes of special polynomial equations arising from two problems from the American Mathematical Monthly; as well as animation for the sake of visual art. Each of these will be exhibited through a series of images and we give the Internet links to the corresponding animations. These sites can be accessed for educational purposes and will be upgraded and expanded from time to time.

Original languageEnglish (US)
Title of host publicationACM SIGGRAPH 2004
Subtitle of host publicationEducators Program, SIGGRAPH'04
Number of pages1
DOIs
StatePublished - Dec 1 2004
EventACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04 - Los Angeles, CA, United States
Duration: Aug 8 2004Aug 12 2004

Publication series

NameACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04

Other

OtherACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04
CountryUnited States
CityLos Angeles, CA
Period8/8/048/12/04

Fingerprint

Animation
visualization
Polynomials
Visualization
art
Internet
interpretation
Education
education
time

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design
  • Education

Keywords

  • Fractals
  • Polynomials
  • Scientific visualization
  • Voronoi regions

Cite this

Kalantari, B., Kalantari, I., & Andreev, F. (2004). Animation of mathematical concepts using polynomiography. In ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04 (ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04). https://doi.org/10.1145/1186107.1186138
Kalantari, Bahman ; Kalantari, Iraj ; Andreev, Fedor. / Animation of mathematical concepts using polynomiography. ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04. 2004. (ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04).
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Kalantari, B, Kalantari, I & Andreev, F 2004, Animation of mathematical concepts using polynomiography. in ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04. ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04, ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04, Los Angeles, CA, United States, 8/8/04. https://doi.org/10.1145/1186107.1186138

Animation of mathematical concepts using polynomiography. / Kalantari, Bahman; Kalantari, Iraj; Andreev, Fedor.

ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04. 2004. (ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - In this paper we demonstrate how a medium called polynomiography, which consists of techniques for visualization of polynomial equations, can be used to animate mathematical concepts, thereby offering a valuable tool for education. More specifically, we will show how it can be used to visualize the following topics: Voronoi regions of points in the plane; multiplication of complex numbers and their interpretation as rotation; sensitivity of polynomial roots as coefficients change; visualization of classes of special polynomial equations arising from two problems from the American Mathematical Monthly; as well as animation for the sake of visual art. Each of these will be exhibited through a series of images and we give the Internet links to the corresponding animations. These sites can be accessed for educational purposes and will be upgraded and expanded from time to time.

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Kalantari B, Kalantari I, Andreev F. Animation of mathematical concepts using polynomiography. In ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04. 2004. (ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04). https://doi.org/10.1145/1186107.1186138