Week 2: Math + Art

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Prior to this week's lecture and course readings, I was unaware of the extent mathematics had influenced art. Without the integration of mathematics into the artistic process, art would not be what it is today. This is especially true since the artistic depiction of the fourth dimension can only be accomplished with the utilization of mathematics. Besides the fourth dimension, I learned about a few other concepts that showcase the intersection of mathematics and art. From Professor Vesna's lecture, I learned about the golden ratio which exemplifies this crossroad. The golden ratio is calculated by dividing a line so that "the shorter part is to the longer part as the longer part is to the whole" (Vesna). The golden ratio can be seen in a number of structures and paintings like the Athenian Parthenon, the Egyptian Pyramids, and Leonardo da Vinci's Mona Lisa.
Da Vinci "The Last Supper" showing golden ratios 

 Also, I learned about the origins of perspective which was originally developed by Indian scholar, Al Haytham, circa 1000 A.D. While he did not apply his theories regarding optics to art, Al Haytham's discoveries were used by Renaissance artists to better develop their artwork. Known for his developments on perspective, Leonardo da Vinci was undoubtedly influenced by Al Haytham.
Leonardo da Vinci's Polyphedra 



Personally, I really enjoyed Robert Lang's origami art and his explanation that the art of origami has advanced due to the introduction of mathematics. Prior to the utilization of mathematics in the art form, origami was merely folding paper. The creative options were limited within origami; however, now, the options are limitless due to the introduction of four mathematical principles into the artistic process. The four rules are as follows: the crease pattern blueprint must have two-colorability; the number of valley folds and mountain folds must always differ by two whether that be two more or two less folds; alternate angles around a vertex surmount to a straight line; there is no self-intersection at overlaps (Lang).
Boeing Icosahedral, Opus 747. Robert J. Lang. 
It is truly amazing what has been and can be created when the forces of mathematics and art are combined. After this week's lesson, it is clear to me that the two are deeply intertwined and that art as we know it today is not possible without the influence of math.
Sources
“Flatland.” Flatland, by E. A. Abbott, 1884, www.ibiblio.org/eldritch/eaa/FL.HTM.

Hart, George W. “Leonardo Da Vinci's Polyhedra.” Leonardo Da Vinci's Polyhedra, www.georgehart.com/virtual-polyhedra/leonardo.html.
Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo. 17.3 (1984): 205-210. Print.
Lang, Robert. “The Math and Magic of Origami.” TED, TED, Feb. 2008, www.ted.com/talks/robert_lang_folds_way_new_origami.

Meisner, Gary, et al. “Golden Ratio in Art Composition and Design.” The Golden Ratio: Phi, 1.618, 24 Sept. 2016, www.goldennumber.net/art-composition-design/.

Tason. “Boeing Icosahedral, Opus 747.” Robert J. Lang Origami, langorigami.com/artwork/boeing-icosahedral-opus-747/.

Vesna, Victoria. “Math + Art.” Lecture 2.

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