It's all fun and games until someone loses an eye.
Monday, July 31, 2006
one-third base times height
Today I had to teach that the volume of a cone or pyramid is one-third base times height. This is not very exciting, and not very intuitive since we weren't proving it, only stating it, and it isn't even intuitive when you prove it (with calculus or with the formula for the volume of a sphere). So I made a model out of cardboard of the three congruent right pyramids that, when put together, make a cube. It was great. I ran out of white cardboard, so I made the inside faces colored, which means that when you assemble the cube, all you can see is white, which kind of helps with putting the cube together if you can't figure out how to do it. The students liked it, as did my master teacher. The pieces don't fit together exactly, but they are close enough to get the point across. I am very proud of my model to illustrate this principle, and I will probably keep my three right pyramids for a long time, if they don't get smushed.
I am a graduate student, working on my PhD in math. I do research and teach calculus to college students. In my free time, I work on becoming an elite distance runner. This blog contains my reflections on math and running, including race writeups.