Week 2: Math + Art

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This week’s lecture was incredibly enlightening, notably the topics on perspective and the golden ratio. In one of my favorite and most influential art classes, I was taught about the theory of perspective by studying some of Filippo Brunelleschi’s works. As stated in the lecture, Brunelleschi’s mastery of geometry and other mathematical principles manifested themselves in his carefully crafted line work and discovery of the vanishing point. These techniques have greatly improved my art ever since learning of them. With this knowledge, I’ve also been able to dissect and reference paintings with ease; you can say I’ve gained an entirely new perspective on the use of math in art.

Filippo Brunelleschi (1377 – April 15, 1446) 

On the topic of geometry, the article “The Fourth Dimension and Non-Euclidean Geometry in Modern Art” by Linda Henderson proved to be a surprisingly interesting read on the matter. Henderson writes about how the concept of the visualization of a fourth dimension was once a form of “liberation” for artists in the early twentieth century, an idea that went on to greatly influence modern art. In this article, I was able to gauge an interconnectedness not only between math and art, but also between art, science, and philosophy. It is quite interesting to see such interplay between disciplines spring from one concept.

In this piece by Picasso, we witness one attempt to capture the fourth dimension through a three dimensional medium, in an art form known as cubism. Specifically, he and other cubists utilized the concept of simultaneity, a way to “simultaneously show views that would not normally be able to be seen together at the same time in the real world.”

   Les Demoiselles d'Avignon - Paris, June-July 1907

The last art piece I’d like to touch upon is the Vitruvian Man by Leonardo Da Vinci. It serves as one of, if not the, most iconic examples of math in art. According to Madiha Jamal’s article on the piece, Da Vinci was able to devise a list of fractions/ratios for the human body (for example: From the hairline to the base of the chin is 1/10 of the height of a man) that coincided with the areas of a square and circle. Although I can say that there definitely exists a juxtaposition between math and art in practice, principles, and in its representation in popular media, it is not as stark as we may think.

Vitruvian Man - c. 1490


Sources:

Da Vinci, Leonardo. Vitruvian Man. 1487, Accademia Gallery, Venice, Italy. 

Frantz, Mark. “Lesson 3: Vanishing Points and Looking at Art.” Cs.ucf.edu, 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. 205–10, https://doi.org/10.2307/1575193. Accessed 9 Apr. 2022.

Jamal, Madiha. “Mathematics in Art - Vitruvian Man by Leonardo Da Vinci.” Medium, Counter Arts, 13 July 2021, https://medium.com/counterarts/mathematics-in-art-vitruvian-man-by-leonardo-da-vinci-edae2989f162.

Kitwood, Dan. “Art History Definition: The Fourth Dimension.” Van Gogh Alive – Genoa, https://www.vangoghgenova.it/art-history-definition-the-fourth-dimension.html

Masaccio. Resurrection of the Son of Theophilus. 1427, Brancacci Chapel, Florence, Italy. 

Picasso, Pablo. Les Demoiselles D'Avignon. 1907, The Museum of Modern Art, New York City, New York. 

“The Fourth Dimension in Painting: Cubism and Futurism.” The Peacock's Tail, 18 Aug. 2016, https://pavlopoulos.wordpress.com/2011/03/19/painting-and-fourth-dimension-cubism-and-futurism/.

Comments

  1. AnonymousApril 10, 2022 at 8:40 PM

    Hi, Anna.

    I really enjoyed reading about the effects that mathematical principles like linear perspective and the golden ratio have had on your own art. I make art myself, and I think I could really benefit from a class like the one that you described. Personally, I found it especially interesting to learn from this week's lecture about al-Haythum, the mathematician who informed much of Brunelleschi's understanding of geometry. I had also learned a bit about Brunelleschi in a past art history class, but never about al-Haythum and I find it really interesting to think about how famous artists and mathematicians have directly influenced one another's work.

    Lastly, I really appreciate your commentary on the Henderson article, as I think the Picasso painting that you included provides a very helpful visualization of just what artists were going for in their attempts to represent the fourth dimension. It's a bit of a difficult idea to digest, but I think your description of simultaneity really helps to give a more concrete example of that bigger idea.

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