Annalisa Crannel has written an interesting article for Inside Higher Ed on using art to teach mathematics. Of particular interest is how artists and mathematicians approach problems differently - the former willing to stumble toward the answer while the latter hold off until they're sure they have the right one.
We all know and can parody the dreaded two-trains problems. A simpler question is this: If you sketch a picture of the rails of the train track going into the distance, and you know where the first two railroad ties go, where do you put the next one? In our class, we change the problem from a horizontal one to a vertical one: the question becomes "Where does the next fence post go?"
It's an easy question to understand, and that simplicity itself makes it unusual in mathematics. It's an obvious question: any artist would want to know the answer. It's even a question that begs to be answered - few people care at all when those two trains meet, but if we want to draw a decent-looking picture of a sidewalk or a fence, then this question about where the next line goes is going to matter to us. It's not obvious what the answer is ... and that puzzle of obscurity lies at the heart of mathematics. This problem is puzzle-solving at its prettiest.
Great post! Thanks.
As an artist and teacher I have used art to get my students to explore math, science and history. It's great to read about teachers in those fields using art too.