horne-scott@CS.YALE.EDU (Scott Horne) (03/17/89)
In article <8817@netnews.upenn.edu> you write: >I wouldn't consder this a puzzle, at least not by the standards of >this group, but the answer surprised me. The puzzle is simple; any high-school student *should* be able to solve it. (No, I'm not so nai"ve as to think that any high-school student *can* solve it.) I once took a course called Abstract Algebra. This was a senior-level course at the university where I took it (not Yale); it was full of grad students and people pursuing teaching certificates in math. One day, the professor stopped talking about groups or isomorphisms or whatever in order to present this problem (and another; see below) to the class. Those math-education majors-- seniors--were *amazed* by the professor's solution of the problem! They copied it into their notebooks and remarked on that ``brilliance'' after class! Anyway, here's the solution: >Imagine that there is a piece of string around the Earth touching >the equator (assume the Earth is shperical). How much longer must >the string be in order for it to be 1 foot off of the equator all >the way around? In other words, how much more string must be added? The Earth (at least under your assumption) is of radius r. The radius of the circle described by the string when extended to stand 1 foot off the surface is (r + 1). The amount of string to be added is the difference between the circumferences: 2 pi (r + 1) - 2 pi r = 2 pi. --Q.E.D. ====== >Do the same thing but this time assume the string is around: > >a) a sphere 2 feet in diameter >b) the sun I did. :-) Since the radius was generalised (`r' instead of the actual value [which doesn't exist, anyway--but that's another story]), this applies to spheres of any size--even ones as small as the brains of the math-education majors who couldn't solve this problem. :-) --Scott horne-scott@cs.Yale.edu ...!{harvard,cmcl2,decvax}!yale!horne-scott 203 436-1756 Box 7196 Yale Station, New Haven, CT 06520 I wish I *could* represent Yale, but Benno Schmidt won't let me....