I get to teach my kids Geometry this summer, and yesterday we did circumcenter, incenter, centroid, and orthocenter constructions. I’ve never done those before, and I was captivated by the beauty of the constructions. I decided to turn a few into watercolors. It was a lot of fun. Here’s another:
In this one I also constructed the orthocenter and the centroid, athought it’s hard to see (they’re pretty close to each other.) Highlighting the construction marks makes it clear that the circumcenter is constructed from the perpendicular bisectors of the lines. It’s not as easy to see that the incenter is constructed from the angle bisectors–I’d love to find a way to show that. This is my favorite way to integrate art and math–using art and design to illustrate mathematical concepts. In many cases a picture is worth a thousand words.
A friend of mine sent me an article about STEAM–the education movement to integrate the arts into STEM (science, technology, engineering, and math) classrooms. I think this is hugely important, although I think it has to go beyond just setting up more discovery learning opportunities. I also think teachers need to realize that engaging in art can be really scary for some kids (just as scary as math is for others!) I advise going slowly. And primary to the whole equation is the relationship between the teacher and her students. When that’s in a good place, you can accomplish just about anything!