OMG! It’s not a Parabola!

For this assignment in my current grad class (Learning Technology through Design) I’ve been asked to explore a problem that was solved by completely redefining the original problem. For some reason I struggled with finding an example for this project. Then, like a sack of bricks, it hit me. One of my favorite youtube channels is Vi Hart’s channel. In the video below she does everything from give math teachers a gut check to making beautiful math art. But the thing that stood out to me had to do with parabolas. She rants about how math teachers spend so much time on parabolas in class and all the different things you could be thinking about while your teachers drones on about them. During this rant she mentions that we often say that projectile motion is parabolic. While for the objects path that we see on earth it can be modeled by a parabola, since the earth is a sphere and gravity is pulling on the object the path is really a piece of an ellipse. Check out the diagrams I made for a visual. (And physics people go easy on me. These obviously aren’t to scale and are only to give a visual that might help solidify the point.)

I had absolutely never thought about it like this. I suppose this may not be as interesting to other people but that reframing really blew my mind. I can’t tell you how many times we have talked about projectile motion in the context of parabolic models. I mean, I know why, but this totally gives me a new, richer perspective on this type of mathematics. She does this at various points in many of her videos. It makes me wonder how much interesting mathematics is being hidden from students because we only give them the stuff that helps them get to the next class. I suppose this might miss the main objective of the assignment a bit, as this doesn’t necessarily solve  a problem. But I think the big takeaway for me in the context of design was perspective. It’s easy to get lost in the details of problems when maybe a different perspective or broader reframing could lead to new revelations.