Tuesday, December 26, 2006

pegs and holes

my family bought a new cabinet and we were placing the top on the cabinet. this was proving difficult as the cabinet makers had not properly aligned the holes on the cabinet with the holes on the top. this lead me to comment that it's like fitting a "round peg in a square hole." there was some dispute concerning this comment. see the video below:

now, obviously there exists round pegs which won't fit in square holes. certainly the main complaint is that the interfaces are not commensurate, and so problems will ensue. the question then becomes which fit is worse: the round peg in the square hole, or the square peg in the round hole?

take your time and think about it.



now, you could just work it out yourself, or you could pull a naive-google, or a thoughtful-google. now, a naive-google would use the result count to determine which statement is used more often, and then say that the statement used more often is likely the better analogy (why would people, since we are such smart beings, use poor analogies? ;) ). so here are the results:

"round peg in a square hole" : 41,700
"square peg in a round hole" : 91,900

so clearly square peg wins out.

now if we do a thoughtful-google and click on some results, we find this problem solving for kids site that after some simple geometry declares:
Hence the circle covers more of the square than the square does the circle. It’s therefore better to be a round peg in a square hole than a square peg in a round hole.
thus, since we want an analogy that describes something that is very difficult to do, we must conclude that i made a weak statement, and should've said it's like fitting a square peg in a round hole.

merry christmas.

UPDATE: someone recently commented that google is dumbing us down, because instead of just working out this simple geometric problem, we just ask google and get an answer that's already written up on the web. certainly there's some merit to this complaint (in this case, though, i worked it out myself because these little problems are fun. indeed, the circle in the square uses a larger percentage of area than the square in the circle). it's very tempting to be as curious as the answers google gives you. however, i also think we can now ask much deeper questions and build on all the knowledge that's easily available.


bea said...

dude, didn't need google to remember that a if a circle and square had the same diameter, that the square's bigger than the circle. :)

One thing you might not know however, is that square cakes are harder to frost and decorate, than round cakes. Think about that one.

merry christmas!!! kisses and hugs for the new year!

omar said...

happy new year!

hmm that's not exactly the problem. the problem is: suppose you have a circle. find the largest square that will fit inside. determine how much area of the circle is unused.

now do the same for a square. fit the largest circle possible inside. what percentage of area is unused?

i contend that it's not obvious which uses more percentage of area.

as to the cakes: why is that? i could make up dumb reasons but i just don't know!