Just came across a really interesting follow up to my recent Calculus without Limits blog..
To tempt your interest, here is a problem:
A bicycle rider is riding in a perfect circle and his wet tires leave two concentric circles on the pavement. (if that is difficult to visualize, see here) What is the area between the outer circle and the inner circle.(the area of the annulus). You are allowed to ask for one measurement (other than the answer) that will allow you to solve the problem. What is that measure.
I came across this little gem following up on some information from a blog at Arjen Dijksman’s Physics Intuitions.
Following up on that and searching around led to a truly interesting MAA article by Tom Apostol about a really interesting approach to a “visual calculus” by Mamikon Mnatsakanian. A really great read for calculus teachers, and students.
The area between the tire tracks is a nice physical application for Mamikon's theorem. There seem to be many more interesting applications, like that parabolic segment area calculation mentioned in the Apostel paper. It's a little disappointing that I've never been told of that method during my engineering studies. I would have appreciated an alternative to calculus.
ReplyDeleteI agree, and I love the parabolic application.. I intend to point it out to my Calc students this year.. I have previously told them about the use of "Polars" to find derivatives of any conic at a given point.. as illustrated in this post
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