I never realized that art contains so much math and geometry until week two’s lecture on Tuesday. Watching Youtube videos and getting to see several examples of these works of art helped me understand the connection math and art have with each other. In Linda Dalrymple Henderson’s article, The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion, Henderson talks about the fourth dimension, which includes more elements such as time, space, and motion.

One of the art projects that I thought related to the fourth dimension was M.C. Escher’s Circle Limit III. Circle Limit III relies heavily on mathematics in order to create its desired effect. Escher’s inspiration for this project came from a mathematician, H.S.M. Coxeter. After its completion, Coxeter mentioned that Escher’s Circle Limit III, which contains hyperbolic tessellations, accomplished mathematical perfection, in which his calculations were correct to the millimeter. Not only does this work of art contain mathematical elements, but it also has elements of space. As your eye moves from the center to the outside of the circle, the fish get smaller, but still maintains its pattern. With the fish getting smaller and smaller, it gives the illusion of looking through a convex lens, thus providing a multi dimensional view on a two-dimensional flat plane.

Another piece of art that I believe is a product of mathematics, perspective, time, and space are kaleidoscopes. A kaleidoscope consists of a tube, mirrors, and small objects. Henderson’s article mentions that Duchamp, an artist, added shadows, mirrors, and virtual images to the four-dimensional vocabulary. The mirrors are one of the main parts of the kaleidoscope, because it allows the objects’ images to reflect around them to create the typical symmetrical effect. To me, this is extremely similar to Escher’s Circle Limit III, in which the objects repeat in a circle with equal angles separating the patterns. What makes them different, however, is that Circle Limit III focuses more on space, while a kaleidoscope focuses more on motion. According to Henderson’s article, “because of the time element in hyperspace philosophy, motion also became in important attribute of the fourth dimension.” One of the main features of a kaleidoscope is to rotate the end of the tube to cause the small objects to move around, which creates new patterns while the entire image is rotating. This creates an element of motion in a kaleidoscope. When I was researching about Circle Limit III, I came across a website that creates a kaleidoscope out of Circle Limit III. I thought it was interesting because it fused these two aspects together.

http://agutie.homestead.com/Files/escher/escher_circle_limit_1.html

Also, according to the American painter, I. Rice Pereira, Einstein’s Relativity is defined as “a ‘pure scientific or geometric system of esthetics.’” This is proof that a kaleidoscope is an example of mathematics with space and art because a kaleidoscope uses geometry to create the images in the shape of a circle, all with equal angles.

I found it extremely intriguing that Escher’s Circle Limit III and kaleidoscopes are related to each other, in which they rely on mathematics, geometry, space, and motion to create a fourth dimension.

http://www.d.umn.edu/~ddunham/dunham.am.pdf