Re: [MATHEDCC] The Potato Salad Problem

Bret Taylor (bret@IAG.NET)
Wed, 9 Apr 1997 20:23:28 -0400 (EDT)

At 10:04 AM 4/9/97 U, you wrote:
>I really like problems like this one for its unexpected answer. I often use
>them (realistic or not) to suggest that we should not always trust our
>intuition. This is always interesting in the midst of a discussion on
>"intuitive" limits.
>
>Another good one involves assuming the earth is a sphere with a circumference
>of 25,000 miles. (I know this is not realistic, but it gets worse.) Stretch
>a string around the equator so that it exactly touches the surface of the
>earth at all points. In other words, take a 25,000 mile long string and put
>it around the earth at the equator. Then add 10 FEET (emphasis intended) to
>the string and form a new larger circle of string that is equidistant from the
>earth at every point. How far above the surface of the earth is the new
>string?
>

I was first presented this problem in a graduate Math Ed course 20+ years
ago (boy, what a memory!!). It was presented with this twist: If you added
50 feet of string to the string stretched around the equator, would it get
far enough off the surface of the earth for an average sized adult male to
crawl under it? If not, estimate how much string you would have to add.

And my, how times have changed. After doing that problem for homework, the
next day we were asked how far a string would rise off the surface of a
tennis ball if 50 feet were added to its length (same situation). So we
were then given the problem to prove that the "new" diameter was a function
only of the "new" length, not of the "old" diameter and to find the equation
relating them. (Does anybody 'prove' anything anymore? ;-) )

>Jerry Thornhill
>jerry_thornhill@sw.cc.va.us
>Southwest Virginia Community College
>Richlands, VA
>
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Bret Taylor Lake-Sumter Community College Leesburg FL

"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden

John 3: 3^3 + 3

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