If anyone out there has a talent for this sort of thing--I have already solved it, I think, but there was some guess work involved. Looking for corroboration.
The problem is to determine the difference in distance around the inner and outer edge of a meandering walking/riding path that circles a lake. It is a "closed loop," but not perfectly circular. For the sake of argument, say the length of the path, along its centerline, is 3.8 miles. The width of the path, for the purposes of this problem, is 7 feet.
Logic tells you the "outer" edge of the path will be longer than the inner edge. But by how much?
Anyone? I'll be watching the comments.
9 comments:
Thinking out loud ...
I bet the problem can be generalized to a circle because inner and outer turns will cancel. If so, then the two circumferences, 2πr(o) and 2πr(i), will differ by 2π(r(o) - r(i)) = 2π7' = 44 feet.
Seems kind of unintuitive because the length of the path doesn't matter. But I think it's right anyway. I'll go with that, and wait and see.
OK, that's what I came up with, complete with the not-totally-formed idea that the meanderings of the path, or even it's length, would have no bearing on the outcome.
My thinking went, the simplest possible path with an inner and outer edge would be one where the inner edge was 0' in length, thus becoming the center of a circle, and the outer edge would be the circumference. From there, I reasoned, any additional length or meandering of said path would, as you said, would vary the inner and outer distances but exactly cancel each other out.
Two great minds . . .
I fully expect Teacake to chime in with some weird theory about how many cookies you could eat while walking along either the inner or outer edge, taking into account shorter steps toward the end of the experiment due to weight gain and general lethargy resulting from hyperglycemia.
What would be weird about that?
I suppose it would work if you also took into account rogue squirrels darting out of the woods and snatching cookies out of your hand.
I will not be chiming in with theories of any kind, cookie-related or otherwise. Because this is MATH. I do not do MATH. I answer questions on 80's movies and the British monarchy.
Great decade for movies, except for possibly Top Gun.
"Hi, I'm Tom Cruise. Do these sunglasses make my head look small?"
"You can be my wing man anytime." *cough*
So you're my Uncle Joey. Better get used to these bars, kid.
Oh god! Don't make me do math.
Post a Comment