Thursday, November 12, 2009 - Saxon Math Strikes Again
Miss Dog Lover is on the final lesson in 7/6, wherein they introduce finding the volume of a cylinder by saying "Imagine pressing a quarter down into a block of soft clay. As the quarter is pressed into the block, it creates a hole in the clay. The quarter sweeps out a cylinder as it moves through the clay. We can calculate the volume of the cylinder by multiplying the area of the circular face of the quarter by the distance it moved through the clay."
At this point I stopped reading, looked at her blank face, and said, "Do you understand what they are talking about?"
Miss Dog Lover, "I understand but it sounds sort of useless. Who would want to put a quarter in clay? It's messy."
Thursday, November 12, 2009 - The Volume of Right Circular Cylinders
Posted by Anyas Friend Me
Messy? No, messy is the problem we discussed in calc one day. We were asking if the volume of a region defined by an equation which was bounded between constraints converged or diverged to infinity. We found that the volume converged to some finite, but presumably quite large number -- we didn't bother trying to calculate it. We found that the surface area of the same region diverged to infinity. In simple English, you could buy enough paint to fill the entire region up -- however, you could not actually coat the surface of the region itself. That was a messy problem -- think how much paint I'd end up spilling all over myself. Now, I wonder how large of a drop cloth I'd need. Would it have to be infinitely large?
