Week 2: Mathematics and Art

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Poor Perspective in Art
https://ayoqq.org/images/perspective-drawing-bad-14.jpg
Art can be understood as the subjective expression of the natural world, and the world that art seeks to imitate and iterate upon as completely defined by mathematics. In this week's lectures, I gained a unique insight into the recency with which mathematics has been directly applied in art. One need only a glance at the image on the right to realize that it poorly reflects reality, yet a true understanding of perspective in art did not occur until as late as the 13th century BCE with Giotto (Vesna). One of the turning points in creating art, especially art that involved architectural objects and scenes as viewed from a close observer's perspective, was the vanishing point (Frantz, 37). The vanishing point is used to convert the visual field, which has disappearing lines due to the perception of vision through the eyes, into an image with lines converging towards certain focal points.
Study for Up and Down
http://platonicrealms.com/images/minitexts/escher/upanddownstudy.jpg
The idea of the vanishing point and perspective was taken to the extreme by MC Escher, who abused the human notion of perspective to create mathematically intensive and extremely complex works of art (Smith). One of his studies, shown on the left, displays the necessity for an understanding of the intersection between mathematics and form in order to create the illusions he is so famous for. In Flatland: A Romance of Many Dimensions, Abbott gives a new perspective to readers by detailing the intricacies of life, romance, and racism in a society entirely composed of 2D shapes (24). In the same way, MC Escher breathes new life in the human perspective of 3D spaces by joining the "surrealist attack on reason and logic" in the 20th century (Henderson, 207). In the coming decades, I believe that mathematics will be intricately intertwined with art through advances in augmented and virtual reality, allowing artists to express themselves in an interactive 4D space and opening up totally new avenues for understanding of our world.
Virtual Reality and the 4D Space
http://prostheticknowledge.tumblr.com/post/130139516771/mirror-m2-tech-art-experience-by

Sources
Abbott, Edwin. Flatland: a Romance of Many Dimensions. SMK Books, 2018.

 Frantz, Mark. “Lesson 3: Vanishing Points and Looking at Art.” Vanishing Points, UCSF, 2000, 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, p. 205., doi:10.2307/1575193.

 Smith, B. Sidney. "The Mathematical Art of M.C. Escher." Platonic Realms Minitexts. Platonic Realms, 13 Mar 2014. Web. 13 Mar 2014. <http://platonicrealms.com/>

Vesna, Victoria. “Mathematics-pt1-ZeroPerspectiveGoldenMean.mov.” Cole UC online. Youtube, 9 April 2012. Web. 13 Apr. 2019. <http://www.youtube.com/watchv=mMmq5B1LKDg>

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