What is the probability that a randomly drawn chord will be longer than the radius of the circle?
(In reply to re(3): Different Approach (Continued)
by Gordon Steel)
Your response is approximate. No one is arguing with that fact. But that is exactly the point. We're looking for an exact answer. Ideally, we always want an exact answer, and rely on approximations only when an exact answer is impossible or too difficult to achieve.
What surprises me most is.... the number of people who seem to be missing the point. Namely: that one can't answer this problem without first specifying what random method one uses to determine the chords. This is the key. There is no 'right' answer, unless we refer to a particular method. And once we specify a particular method, we should be able to achieve an exact answer.
As for your question about the Origami... please keep comments about that problem in the same problem's comment list. The solution will be posted shortly, no doubt. But in the meantime, I suggest you READ the other comments (such as this one or this one), which suggest ways of determining the answer, and in fact, specify the answer. You can verify that way, whether or not you came up with the same answer.
Edited on October 15, 2003, 5:59 pm