Unit 2: Math and Art

I was very interested to learn how math and art are related since they have always been two completely separate topics in my life (especially in engineering). After watching Professor Vesna's lectures, I realized math and art are related in such a way that math can be used to explain how to transcribe three-dimensional space onto a two-dimensional canvas. The most prominent feature is the vanishing point. This point is "the intersection of the projections of two parallel lines in space onto the picture plane" (Anderson 2007). Marc Frantz provides an excellent visual showing how the vanishing point works in reality.

If this person can only see in one dimension, the person is able to see the line L when he looks in any direction not parallel to the direction of the line. As the difference between the angle of his sight and the angle where he sees the vanishing point reaches zero, the distance at which his line of sight intersects line L approaches infinity.

A similar phenomena occurs in Edwin Abbot's "Flatland". Edwin states, "Take for example an equilateral Triangle... Figure 1 represents the Tradesman as you would see him while you were bending over him from above; Figures 2 and 3 represent [how] you would see [it] if your eye were close to the level... and if your eye were quite on the level of the table". As the angle between your line of sight and the table reach zero, any depth of the object vanishes. 

Furthermore, art and math coincide when discussing the Golden Ratio. The Golden Ratio is the ratio of two line segments where "the longer part divided by the smaller part equals the whole length divided by the longer part" ("Golden Ratio" 2014), which equals approximately 1.618. 

We see that the golden ratio was used when constructing the Parthenon, where "each of the grid lines is a golden ratio proportion of the one below it" (Geisner). The ratio was also used when Leonardo Da Vinci explained the ideal proportions of a human body. It surprises me that using the golden ratio on objects can make the objects more aestethically pleasing.

I now understand a little bit more how art used mathematics during the Renaissance era and earlier to draw more accurate depictions of reality. However, I am curious to know if any modern mathematics is used in modern art, or vise-versa.

References:

Anderson, Kristi. Geometry of an Art. New York: Springer, 2007. Print.

Frantz, Marc. "Lecture 3: Vanishing Points and Looking at Art." University of Central Florida, 1 Jan. 2000. Web. 12 Apr. 2015. <http://www.cs.ucf.edu/courses/cap6938-02/refs/VanishingPoints.pdf>

A. Abbott, Edwin. "Section 1 Of the Nature of Flatland." Flatland, by E. A. Abbott. 1 Jan. 1883. Web. 12 Apr. 2015. <http://www.ibiblio.org/eldritch/eaa/F01.HTM>

"Golden Ratio." Golden Ratio. 1 Jan. 2014. Web. 12 Apr. 2015 <https://www.mathsisfun.com/numbers/golden-ratio.html>.

Meisner, Gary. "The Parthenon and Phi, the Golden Ratio." Golden Number. 20 Jan. 2013. Web. 12 Apr. 2015. <http://www.goldennumber.net/parthenon-phi-golden-ratio/>.