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Buffon's Needle
By Clare Nicholson (P1732) on Thursday, February 10, 2000 - 06:27 pm:

Hi, I'm Clare I and I was wounderin' if anyone's heard of "Boffin's Neadle?" I know what u have 2 do but any facts at all would be great.

Oh it is when you drop a needle or somethin' similar one a piece of paper that has lines drawn on it the width(of the line)of the length (of the neadle) of the neadle (If that makes sense!) It is similar to the black and white lined 2p arcade game were usless it fits perfectly on a movin' conveabelt inbetween the lines u lose ur money otherwise you win more.

Ok C U soon
Clare

By Alastair Fletcher (Anf23) on Thursday, February 10, 2000 - 10:32 pm:

Hi Clare,

Buffon's needle problem is one experimental way of finding a value for pi.

If you drop a needle of length p at random onto a floor marked with parallel lines a distance m apart (and you have to have p smaller than m), then the probability that the needle intersects one of the lines is (2×p)/(p*m).

Actually showing this involves a bit of calculus, so I guess that you'll have to take it on trust that this is true.

So, you know the length of the needle and the distance between the parallel lines, so if you repeat the experiment lots of times, you'll be able to approximate p.

Hope that helps,

Alastair

By Clare Nicholson (P1732) on Friday, February 11, 2000 - 04:23 pm:

Thanx Alastair,

I had to drop a needle on a piece of paper with lines on it 100 times. 29 times it landed inbetween the other 71 times it touched the lines.

Clare

By Richard Mycroft (P2053) on Friday, February 11, 2000 - 07:38 pm:

Hi Clare,

Does the length of the needle have to be at right angles to the parallel lines or is the angle random?
What were p and m in your experiment?

Richard

By Clare Nicholson (P1732) on Friday, February 11, 2000 - 10:51 pm:

Yeah I know you need to know the length of the needle but I measured it! It was somethin' like 3.6cm. How do you use that.

If this experiment is somehow is based on pi, then it must have somethin' if very small to do with circles. I am assuming that the length of the needle is the diameter. But I sort of see your point.

The needle is dropped from a height this was not an exactly accurate experiment and the height was roughly the same at all times but was not actually measured.

But the thing I think some r not understanding is that p was the length of the needle and m was the distance between the lines, p = m. They were the same.

Ps. Please do not go into great detail cause I'm only 13 and do not understand everything that is goin' on about 2×p / by pi×m!! Please help me and please keep it as simple as possible!

By Alastair Fletcher (Anf23) on Saturday, February 12, 2000 - 02:40 pm:

Hi again,

As long as you keep the length of your needle and the distance between the parallel lines the same, then the probability that you land on one of the lines is 2/p, which my PC's calculator tells me is about 0.64 (since p is about 3.14). So, you've got a 64% chance of landing on one of the lines, which is pretty close to what you got, Clare.

Richard - I'd be very surprised if you could drop a needle and get it to land exactly at 90 degrees to the parallel lines!
You get something to do with p in the answer precisely because the angle that the needle lands at is random.
I don't think it matters all that much what height you drop the needle from as long as it isn't from really low.

Alastair