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Solving Problems by Factoring

Factor and use the zero product rule

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Polynomial Art

Credit: Lasse Rempe-Gillen
Source: http://commons.wikimedia.org/wiki/File:Julia_set_of_the_quadratic_polynomial_f(z)_%3D_z%5E2_-_1.12_%2B_0.222i.png
License: CC BY-NC 3.0

Can a polynomial be beautiful? A computer scientist from Rutgers University uses polynomials to create art. Dr. Bahman Kalantari has developed a computer program that visualizes solutions to complex polynomials. He calls his work “polynomiography," and he's shown his paintings and movies at museums and galleries in the United States and Europe.

Solving Equations, Creating Patterns

Both math and art use patterns to help people understand the world. Dr. Kalantari realized that patterns and images could help him see how computers solved complex polynomials. Computers use a guess-and-check method to find the roots to complex polynomials. Some programs are better at solving polynomials than others. Dr. Kalantari wrote a program that creates a picture based on a computer’s attempts to solve polynomial equations. The user can choose a method for the computer to use, as well as a color scheme. After the computer has completed the image, the artist is free to modify the colors and highlights of the result in order to create a more impressive piece of art.

Credit: Sydney Missionary Bible College
Source: http://www.flickr.com/photos/smbcollege/5510558786/
License: CC BY-NC 3.0

Dr. Kalantari uses polynomiography to teach high school and college students about polynomials. He hopes to show others how beautiful mathematics can be through his art. He also uses polynomiography in his own research. The art form enables him to see new ways of approaching complex polynomials.

See for yourself: http://www.youtube.com/watch?v=TpYHUkSCi-s

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Watch one of Dr. Kalantari's movies below. How else could you use algebra as the starting point for a work of art?

http://www.youtube.com/watch?v=kMP0vclKlDA

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Image Attributions

  1. [1]^ Credit: Lasse Rempe-Gillen; Source: http://commons.wikimedia.org/wiki/File:Julia_set_of_the_quadratic_polynomial_f(z)_%3D_z%5E2_-_1.12_%2B_0.222i.png; License: CC BY-NC 3.0
  2. [2]^ Credit: Sydney Missionary Bible College; Source: http://www.flickr.com/photos/smbcollege/5510558786/; License: CC BY-NC 3.0

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