Kramerica Industries, How To Turn A Rectangle Into A
Circle
The idea for this talk came from the basic Calculus I question
of “Given x feet of fencing, maximize the area enclosed.” A student asked me if we could enclose more
area if we used a circle instead of a rectangle. I asked him to check for himself and sure enough, he realized
that yes we could.
That
being said, this is a project that I give to my Calculus I students. I send them a letter from Kosmo Kramer
asking for their help determining the maximum possible area that can be
enclosed with 800 feet of fencing. The
students immediately respond with a 200 by 200 square and think that everything
is decided. We then have in-class
discussions about topics such as “What if he has a barn, a river, etc.” From there I lead them into a discussion of
using more than four sides for the enclosed area. After this, (hopefully) someone says “Sure, but how do you make a
circular fence?” This then takes us
into considerations of how many sides we could make practically speaking. It ends with a discussion of creative uses
of the barn, which is 75 feet by 75 feet.
There is clearly an emphasis on student discussion throughout
this process. The finale of the project
is a paper that they must write, not to me, but to Kosmo Kramer, who knows
nothing about Calculus. They need to
try and explain the entire process of our discussions to him in a manner easily
understandable to a layperson. This
project has worked wonderfully for me in helping the students learn how to
approach a typical max/min problem, limits, and perhaps most importantly,
solving a problem without a specifically chosen technique. I encourage them to think of new approaches
to this question and “Think outside the box.” (Pun intended)