Back to Blog
Psequel columns not showing up5/31/2023 ![]() What is more, provided you know the formula for the volume of a sphere, that alternative derivation makes no use of calculus at all! Once you have solved the problem the pedestrian way and found the formula for the volume of the napkin ring, it doesn't take most mathematically able individuals long to come up with another derivation. ![]() For the moment, let me see if we can do as Lockhart would hope and figure out just what is going on with the napkin ring. In that essay, Lockhart argued for teaching that awakened and stimulated students' natural curiosity. My March column, which was devoted to publication, for the first time, of an essay he had written back in 2002. I must have watched too many episodes of Prison Break.) The question is, what is the student's response on seeing that surprising answer? Mathematics teacher Paul Lockhart would hope - wish - that the student would be prompted to ask "Why?" and would then seek to find an explanation. It's a routine application of integration. Any student who can carry out the calculation I gave has demonstrated mastery of the technique for calculating a volume of revolution. ![]() There is nothing difficult about it, and it does provide a perfectly good exercise in integration. The proof I gave at the time was (deliberately) the "by the book", pedestrian one. The volume of the napkin ring does not depend on the radius of the sphere from which a cylinder is removed to create the ring, but only on the height of the cylinder. Last month's column I discussed a classic calculus problem often referred to as the "napkin ring problem." Although it appears at first glance like any one of dozens of volumes or revolution problems that calculus instructors give their students to practice their mastery of integration, this particular problem has a surprising answer.
0 Comments
Read More
Leave a Reply. |