Unit 2: Math + Art

Leonardo da Vinci's Vitruvian Man - a study on the human body, proportions, and perspective
https://www.leonardodavinci.net/images/gallery/the-vitruvian-man.jpg

Math was one of my favorite subjects when I was younger – I spent my free time devouring puzzle books and competing in creative math. The boundless power of math, and its position at the core of scientific knowledge, was fairly obvious to me. However, I never fully considered the extent of math’s impact through its influence on art as well. I knew about artistic elements such as perspective and the golden ratio (Vesna). What was new to me was the notion that these concepts, rather than being rooted solely in the world of art, derive from a blend of mathematical principles, scientific ideas about optics, and artistic depiction. Leonardo da Vinci embodies the harmony between these three fields, as an avid artist, mathematician, scientist who applied his varied interests to reach unparalleled heights of artistry and creation. 

Mandelbrot set
https://upload.wikimedia.org/wikipedia/commons/2/21/Mandel_zoom_00_mandelbrot_set.jpg

I realize now that this week’s unit broadens ideas I have been exposed to in the past. I remember watching a film adaptation of Flatland in middle school. After reading the original work by Abbott, the idea of Flatland sheds light on not only geometric and artistic perspective, but also the boundaries of what we (think) we see and know. Another concept I was pleasantly surprised to encounter again was fractals. I had seen them in math classes (the Mandelbrot set was actually the cover of my calculus textbook!); but the videos on fractals helped me appreciate the mathematical complexity and beauty of these phenomena, and their prevalence in the natural and artistic worlds. I was especially intrigued to find out the relationship between fractals, Fibonacci numbers, the golden ratio, and the stock market (Socioeconomics Institute). The idea that human activity can be modeled through these functions demonstrates the power of math, art, and science when they work together.

Mathematical process behind origami
https://www.oh-i-see.com/blog/wp-content/uploads/2014/03/four-step-process-1024x499.jpg

I was also fascinated to learn about the connections between math and origami. Robert Lang’s talk brought a new perspective to this craft as a synthesis between art, math, and engineering (Lang). The idea that you can create any shape by applying the mathematical principles of two-colorability, vertex folds and angles, and layer ordering brings to light how the rationality of math can enhance the imaginative creativity of art. That this relationship can be extended to applications in science and engineering illustrates how vital art, math, and science are to expanding their respective fields, and how their fusion can advance the progress of humanity.

References

Abbott, Edwin A. Flatland: A Romance of Many Dimensions. Princeton, N.J., Princeton University Press, 1884.

DlimitR. “Fractals – Mandelbrot.” YouTube, 17 June 2006, https://www.youtube.com/watch?v=ivRQDbAduoM.

Lang, Robert. “The math and magic of origami.” TED, Feb. 2008, https://www.ted.com/talks/robert_lang_folds_way_new_origami#t-850189.

Socioeconomics Institute. “Fibonacci, Fractals and Financial Markets - Socionomics.net.” YouTube, 31 May 2007, https://www.youtube.com/watch?v=RE2Lu65XxTU.

Vesna, Victoria. “Mathematics-pt1-ZeroPerspectiveGoldenMean.mov.” YouTube, uploaded by uconlineprogram, 9 April 2012, https://www.youtube.com/watch?v=mMmq5B1LKDg.