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Jun 17, 2019
For the past two months, I have been teaching art in a local elementary school, in classes from kindergarten through sixth grade. Thanks to the local PTA, I was able to work with each class several times, enough to get to know the students and teachers. One thing I discovered is that the pleasure one feels when creating art oneself is magnified 100 times by being in the presence of 30 people creating art happily. To give someone a chance to lose themselves in a subject is a wonderful thing for a teacher.
Unexpectedly, in these last months, I experienced the strong connection between art and mathematics. Before teaching these students, I would have said the benefits of art are the following: 1) honing your creativity, 2) opening your mind, and 3) developing your hand-to-eye coordination. The last thing I would have said is that art can teach you math. Well, I have totally changed my mind, now. Art is math, baby.
Here are some examples of math in art. To help the students scale their drawings, I brought pictures to copy that had a grid already imposed on them, like this bunny:
The idea I intended to use with the students was that they would draw the same grid (3x3, or tic-tac-toe) on their paper, and then they would know where to start drawing each part of the bunny.
Here's an example of how to draw the bunny's ears on the grid:
Naively, I assumed that drawing the grid would take a nano-second, and then we could move on to adding the bunny. Quickly, in the first class, I sketched a sample grid like this on the board:
However, many students were not used to creating a grid in thirds of equal sizes, and drew grids more like these:
In both of the cases above, the students struggled with the right proportion for their nine parts. We had to slow down and get the grid right, because otherwise the bunny would come out looking like a dachshund. Why could the students not draw the grid? I can attest that they have excellent teachers, but as it turns out, dividing a paper by thirds is not something that non-artists do a lot in regular life. For example, reader, when was the last time you drew a 9 square grid of equal sizes on a sheet of copy paper? Probably, the last time you played tic-tac-toe in, like, 1990.
The same problem happened with circles. When I asked the class to draw a circle and divide it into three parts, I expected lots of drawings like this:
Instead I got a lot of drawings like these:
After this happened in every class, in every grade, I had to conclude that matching proportions in drawing, even in simple geometric shapes, is a skill that has to be honed over years. All though most students instantly grasp the concept of "rectangle" versus "square" when shown a picture of a square, they struggle when actually forced to draw the shape with their own hands. Knowing something conceptually is not the same as knowing it by muscle memory.
You may be thinking "Well, duh!" but to an adult artist like me, the hard shapes are all non-geometric, like the human face, a spirally tree or a crashing wave with a thousand drops. As a teacher, I was suffering from expert blindness syndrome, for I did not factor in the years I must have spent learning to draw grids in perfect proportion.
Lastly, I did not pick a 9 square grid by chance. Professional camera lenses have this grid imposed on them. Dividing a composition by thirds is extremely important in Western painting, as pictures based on thirds will align with Nature's golden ratio and seem more beautiful. Here are some famous examples you may have seen, below. It was no accident that they are all composed in thirds. That's the lesson for today reader: drawing helps you learn math. Just ask Leonardo.
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