Math and Art

        Math and art, the two subjects that seem like in different paths, are actually inextricably linked: Math is commonly found in our life, and our life is made of art.

        The first thing that I think about related to both math and art is perspective: the parallel lines in 3D world drew on a 2D surface will converge to one point, which can be also stated as the Vanishing Point Theorem: "If two or more lines in the real world are parallel to one another, but not parallel to the picture plane, then they have the same vanishing point"(2). According to the lecture, "Perspective is necessary in order to understand painting. It is completely mathematical." It is interesting to compare this with the novel Flatland by Edwin A. Abbott: the 1D line from lineland can't understand the world of 2D square from flatland, and similarly, the square can't understand the world of a 3D sphere. However, in painting, prescriptive perfectly connects three dimension world with two dimension world.

        Fractal is also a mathematical set that exhibits a never-ending artistic pattern. Mandelbrot fractal is the most popular one that generated from a very simple formula: z=z^2+c. Its boundaries not only contain miniature copies of the whole set, but also have a truly infinite variety of different shapes. The shapes include tree, rivers with lakes, galaxies and waterfalls. All of these are art!

        When we look at a specific art, the Japanese paper-folding origami, we will find the connection again. Such as alternate angles around a vertex sum to a straight line, and skinnier flap leads to a circle etc. Artists use the patterns or rules to create forms. With computer program, we can design different origamis on demand, such as the Japanese solar array flew in 1995. At this point, we can see the influence of mathematics in art and science.

        Mathematics, art, and science are in juxtaposition. They are inseparable. Just like the relationship between the two cultures, only when we understand the connection among mathematics, art and science can we make further progress in our society.

Abbot, Edward A. Flatland: A Romance of Many Dimensions. 1884.

Lang, Robert. "Robert Lang: The math and magic of origami.” TED. Feb. 2008. Web.  10 April 2015. http://www.ted.com/talks/robert_lang_folds_way_new_origami?language=en

Lesson 3: Vanishing points and looking at art. Marc Frantz 2000.

Fractals - Mandelbrot. "https://www.youtube.com/watch?v=ivRQDbAduoM#t=99" Youtube, 17 Jun. 2006.

Vesna, Victoria. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." YouTube. YouTube, 9 Apr. 2012. Web. 12 Apr. 2015.