Week 2: Math + Art (Travis Shibata-Bardaro)

Mathematics has a long history of influencing the arts and sciences. For example, in 1413, Brunelleschi correctly formulated linear perspective by use of a single or multiple vanishing point(s) (Vesna 11:14). Vanishing points, which are represented in Figure 1, are points in which all parallel lines in a plane converge (Frantz 1). While the architectural lines of the real-world building are parallel, the images of such lines are not since they intersect at the vanishing point (Frantz 1). Overall, the vanishing point implements both geometry and the science of optics to form a perfect three-dimensional image on a two-dimensional canvas (Vesna 12:44). Past the three-dimensional, both artists and scientists were interested in concepts surrounding the fourth dimension and what it may entail. For artists, the fourth dimension symbolized liberation, allowing them to reject one-point perspective systems (Henderson 205).

Figure 1: Frantz, Marc. “Locating Vanishing Points.” UCF.edu, 2000, http://www.cs.ucf.edu/courses/cap6938-02/refs/VanishingPoints.pdf. Accessed 13 Apr. 2023. 


Then there is the Vitruvian Man, which is a drawing based on conceptions of ideal human body proportions according to the architect Vitruvius (Vesna 26:38). The drawing of the Vitruvian man is often associated with a combination of art and science, which suggests a sort of interchangeability between the sciences and math. 

Figure 2: Da Vinci, Leonardo. “The Vitruvian Man.” LeonardoDaVinci.net, https://www.leonardodavinci.net/the-vitruvian-man.jsp. Accessed 13 Apr. 2023. 


In a more contemporary light, math, science, and art all come together in the form of origami, oddly enough. Figure 3 is a crease pattern that is used to make a Mosquito. These crease patterns are obtained from mathematical functions such as circle or square packing (Lang, “11 Levels” 10:16). The complexity depends on the total number of folds along with the number of folds that are brought together at once (Lang, “11 Levels” 0:14). How these designs are made based on mathematical principles is beyond my knowledge; however, they also prove useful within the sciences. For example, Lawrence Livermore National Laboratory wanted to make a space telescope with a lens that was 100 meters in diameter and 25,000 miles above the Earth (Lang, “The Math” 11:56). The issue was that a rocket ship was much too small to carry such a large lens, so the solution was to somehow fold the lens into a more compact shape (Lang, “The Math” 12:24). By collaborating with origamists such as Robert Lang, together they were able to develop a pattern that allowed the lens to fold into a compact cylinder (Lang, “The Math” 13:05).

Figure 3: Lang, Robert J. “Crease Pattern of AEDES AEGYPTI, OPUS 619.” Robert J. Lang Origami, https://langorigami.com/crease-pattern/aedes-aegypti-opus-619/. Accessed 13 Apr. 2023. 

Figure 4: Lang, Robert J. “AEDES AEGYPTI, OPUS 619.” Robert J. Lang Origami, 2012, https://langorigami.com/artwork/aedes-aegypti-opus-619/. Accessed 13 Apr. 2023. 


Here, mathematics achieves the spot of the third culture as through it, science and art are able to effectively communicate, yet each subject is still faintly distinguishable.


Works Cited

Frantz, Marc. Lesson 3: Vanishing Points and Looking at Art. University of Central Florida, 2000, https://www.cs.ucf.edu/courses/cap6938-02/refs/VanishingPoints.pdf.

Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, pp. 205–210., https://doi.org/10.2307/1575193.

Lang, Robert. “11 Levels of Origami Easy to Complex | WIRED.” YouTube, uploaded by WIRED, 20 November 2019, https://www.youtube.com/watch?v=MDwPXRy9IFc. Accessed 13 Apr. 2023.

Lang, Robert. “The Math and Magic of Origami.” TED, 2008, https://www.ted.com/talks/robert_lang_the_math_and_magic_of_origami?language=en&subtitle=en. Accessed 13 Apr. 2023.

Vesna, Victoria, director. Mathematics-pt1-ZeroPerspectiveGoldenMean.mov, UCLA, 9 Apr. 2012, https://www.youtube.com/watch?v=mMmq5B1LKDg. Accessed 13 Apr. 2023.

Comments

  1. Georgia PhillipsApril 16, 2023 at 7:04 PM

    Hi Travis! Great job you fit so much into one post, it really exemplifies the concept of this week and the juxtaposition of mathematics, science, and art. I really enjoyed your example you included with the Vitruvian man I think that really stood out as a great example from this week.

    ReplyDelete

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