The Colorful Four Color Theorem

 

There is a certain kind of art behind the graph coloring and the four color theorem. I mean, of course it is because there is actual color being used in a math problem. Math, where usually you have to add and subtract numbers. This painting above, created by Piet Mondrian, does not exactly represent the four color theorem. There are edges touching that share the same color, so that of course would not work in the color theorem. But this painting was done in 1930, and the four color theorem wasn’t approved until 1976. When you compare the oil painting to an actual four color theorem problem, at first glance you might jus consider both of them to be pieces of abstract art. Of course once you take a closer look, you can see that math problem behind the picture on the right. “In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.”  So maybe Mondrian wasn’t trying to achieve the four color theorem with his oil painting, but he was getting close. There is math everywhere, even in art. Or sometimes the math problem turns into the art.

3 Replies to “The Colorful Four Color Theorem”

  1. Reading this post and being in class has made me intrigued about how art can be created using math. I find it so fascinating how math problems and theorems can become the basis for paintings, poetry, and even music. Seeing as how we have been focusing on drawings and paintings, I was looking up math in art and found a painter named Crockett Johnson who used multiple theorems and experiments to create his masterpieces. Through the following link, you can see online versions of his work, and all of them include the reasons why he made each one. My favorite is titled “Squares of 1, 2, 3, 4 and Square Roots to 8”, where the painting uses shades of blue to reflect what looks like a multiplication times table, although the painting makes it look like ripples in the water, at least in my eyes.

    Link: http://americanhistory.si.edu/collections/object-groups/mathematical-paintings-of-crockett-johnson?page=3

  2. This makes me wonder about how much art you could “rationalize” into systems or patterns of math. Coming from more of a philosophical background I wonder how much this rationalizing is healthy and useful for society and how much isn’t. Is there a limit to how much we can make sense of the world with patterns as as humans have created? Given how far individuals imaginations can go, the answer is, probably not. Interesting stuff!

    Also worth noting mathematical artistry is an entire genre!

    https://en.wikipedia.org/wiki/List_of_mathematical_artists

  3. Wow I never would have made the connection from that painting to the 4 color theorem. I love that painting and have been a fan of it for a long time now. It is amazing how close Mondrain got to the four color theorem without even realizing it. Looking back on art work I have seen in museums you can see the math in works that you would normally think are just random. to me that is so amazing because who would have thought that learning math would open up your view on certain art pieces.

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