Week 2: Math + Art

Applying mathematical principles to art helps shape artists’ perspectives and interpretations. In Flatland, Abbott uses geometry to portray society and gender, where women are line segments and men are many-sided figures (Abbott 4-5). Abbott created a fictional two-dimensional world where social stratification is determined by the shapes’ number of sides; ultimately, the highest status is a sphere, a three-dimensional object. Abbott’s interpretation of society demonstrates the difference in perspective through mathematics. For example, women are line segments, but from a side view, they are only a single point (Abbott). Abbott’s social hierarchy suggests that lower levels of the hierarchy will not understand a higher level’s perspective, such as with two-dimensional versus three-dimensional object. Perspective allows artists to get a better understanding of the world.

4D Art by Tony Robbin
http://fourdimensionalart.blogspot.com/
In addition to three-dimensional space, there exists a fourth dimension. This fourth dimension have “encouraged artists to depart from visual reality” (Henderson 2), thus creating abstract art. Human beings cannot visualize the fourth dimension; therefore, mathematics depends on art for visualization.   
Art by Piet Mondrian
https://www.pinterest.com/magdalenaurbank/piet-mondrian/

Piet Mondrian is known for using geometry and primary colors in his abstract pieces (Uconlineprogram). His work uses geometric shapes to build other shapes. Mondrian uses proportion and scaling to create his work. His art conveys reality and logic by expressing a balance in the world based on how the shapes are drawn. The horizontal and vertical lines can be interpreted as opposing forces in the world, since horizontal and vertical lines move in different directions and are displayed differently.

  
Lung Fractals
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgFT1a4CwtWmp6Pb790sGH2ROZBreNpyE9h4u4F24xaI-oMvxfwR2Xdhg76Bnwa1s12xMLmtHQ77u6_s7MUCZg-Q56lExZrOooYZJEClEoam7-ywTQavv_7R95Z34nT5lijpeRKoi3fKA/s1600/ralph-hutchings-resin-cast-of-the-human-lungs-and-bronchial-tree.jpg

Mandelbrot Set, a type of fractals – object with self-similarity – is another example that demonstrates mathematical art (Weisstein). Fractals can be represented by an iterative equation: z = z2+c (DlimitR).  Mandelbrot set continues infinitely (“Mandelbrot Set”). Since it increases to infinity, art can portray the idea of a fractal clearly by showing the pattern within that one pattern. Understanding fractals, artists will have a deeper sense of patterning and for example, can create a biological model of blood vessels of the lungs.

Mathematicians and artists both depend on one another for interpretation and concrete representation. This connection between math, science and art is significant. Art is a visualization tool for science and math; math and science work to interpret meaning and provide proof for abstract work. The contribution of all three cultures helps create a well-understood world.


References
Abbott, Edwin A. "Flatland A Romance of Many Dimensions." Flatland: A Romance of Many Dimensions. N.p., n.d. Web. 16 Apr. 2017.
DlimitR. "Fractals - Mandelbrot." YouTube. YouTube, 17 June 2006. Web. 16 Apr. 2017.
Henderson, Linda Dalrymple. "The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion." JSTOR. The MIT Press, n.d. Web. 16 Apr. 2017.
"Mandelbrot Set." Mandelbrot Set -- from Wolfram MathWorld. N.p., n.d. Web. 16 Apr. 2017.
Uconlineprogram. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." YouTube. YouTube, 09 Apr. 2012. Web. 16 Apr. 2017.
Weisstein, Eric W. "Fractal." From MathWorld--A Wolfram Web Resource. N.p., n.d. Web. 16 Apr. 2017.

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