In alignment with my portfolio foreword, I started research on the broad topic of mathematics in art. Though I initially thought that there wouldn’t be much to talk about, I realized I was very wrong. On the contrary, the results I churned out were overwhelming – not to mention, complex and abstract.

The artist I ultimately decided to base my research on was renowned M.C.Escher. I first learnt of him during my art theory lessons in school, and my research went from there. Escher’s work has been enjoyed by millions all over the world, and can often been found on the internet.

 Clearly illustrated in Reptiles (1943), Escher’s work incorporates mathematical concepts, most prominently, intricate and complicated tessellations. Indeed, Escher’s journey in the Mediterranean was what sparked his interest in mathematics and art. To be more exact, Escher was interested in symmetry and order. Often, he would build is artworks on impossible geometric objects such as the Necker cube and the Penrose triangle. He stumbled across George Polya’s academic paper on symmetry groups, and soon became intrigued about the 17 plane symmetry groups, also known as the 17 wallpaper groups. In 1937, he started incorporating this concept into his woodcuts.  

In order to aid himself in his quest to apply mathematical concepts in art, Escher wrote the paper, Regular Division of the Plane with Asymmetric Congruent Polygons. In the paper, he discussed colour based division and developed a system of categorizing combinations of shape, colour and symmetrical properties. The study of these areas later became known as crystallography.

In 1956, he met with Canadian mathematician, H.S.M. Coxeter whom inspired Escher’s interest in hyperbolic tessellations, the regular tiling of hyperbolic planes. This is illustrated in the picture, Circle Limit IV.

Because of Escher’s inherent dislike of flat planes, he went on to do more research on dimensions. Often, he would include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, or he would combine 2-dimensional images with 3-dimensional images, as evidenced in the above image, Reptiles. He also went ahead to study the concept of topology, under the tutelage of British mathematician Roger Penrose, he learnt additional concepts that enabled him to create his famous Waterfall and Up and Down. As we can see in Waterfall, the water falls from a higher level, down to a water wheel which then leads to a path where the water flows through. But as our eyes follow the path, we then realize that it is this path that leads to the waterfall! How is this possible! This is why Waterfall amazes me.

I am very glad that I decided to do this research. While we did talk about M.C.Escher in art theory, we only touched a small aspect of his artworks. Through this research, I found out a lot about how math can be incorporated into art, and I have to say that Escher has managed to do this incorporation exceedingly impressively. I wish I had done this research earlier, if I did, I might have chose to incorporate math into my art coursework! Well, this has inspired me to try out a more complicated tessellation. (I hope seeing his artworks have inspired you to try out as well, Ms Yeo!)

If I had more time, I would have dearly liked to research about more artist who have successfully incorporated math into art. For example, I found out that there were people who could create art with math on computers. These are interesting geometric shapes and concepts I would have liked to look into, for example, fractals and the additive blending concept by R. Hodgin.

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Math in art. I actually did this for my math portfolio, but I’m just stuffing this here anyway. -.-lll Oh gosh, I sound retarded in the piece. -.-