- 19 Apr '06 02:20 / 2 edits

At first glance I would say the answer is the following:*Originally posted by Codfish***How many non-intersecting chords of length N can fit into a circle of radius R?**

P.S. If you don't know what this means, don't even try.

P.P.S. Show your work or you'll get no credit

1, if N = 2R.

The nearest whole number that is less than or equal to Pi/[InverseSine(N/2R)], if N < 2R.

Is this what you got?

Edit: To get the above answer, I am simply dividing 2*Pi by the angle ACB, where A and B are the terminal points of some chord of length N, and C is the center of the circle. - 19 Apr '06 04:04 / 1 editSorry lemon Jello, I missed your post. (Somehow)

That is indeed what I got. Please note, though, that the maximum side length for each maximum #of chords is .................................................................

Never mind, its too obvious for me to say it out loud without being blinded

:'( - 19 Apr '06 20:50 / 1 edit

By intersect do you mean its not allowed for even the ends of the chords to touch? I think even if that were the case you still could get an infinite #, they can asymtotically approach each other not touching, but infinitely close. Don't see a limiting factor here.*Originally posted by Codfish***No, because they are all of the same length and can't intersect**

For every chord you can construct there would be a smaller one that could be fitted in the same space, ad infinitum. - 19 Apr '06 22:19 / 3 editsWait, unless N (the length of the chord) is fixed. in which case it is not infinity, there would have to be a relation between N and R. I'm an idiot, i just got the same answer as LemmonJello. Sorry. So in response to sonhouse draw a picture and you'll see it is not infinite, N has to be fixed.
- 19 Apr '06 23:16

Yes, N is a fixed length. Sorry for the confusion*Originally posted by frew***Wait, unless N (the length of the chord) is fixed. in which case it is not infinity, there would have to be a relation between N and R. I'm an idiot, i just got the same answer as LemmonJello. Sorry. So in response to sonhouse draw a picture and you'll see it is not infinite, N has to be fixed.**