Saturday, April 14, 2018

Boffon's Needle



Boffon's Needle


This experiment used integrals to calculate the probability of a needle being dropped on a sheet of paper with lines drawn on it landing on a line. I don't care about that, except that in 1777 The Comte De Buffon (Georges-Louis Leclerc) figured that the probability of a needle landing on a line is two divided by Pi.

So here's what I did: I found a box of needles (pins) that were 3/4" long. Then I drew lines on a piece of paper spaced at 3/4" from each other. This makes the needle and the space both 3/4" and thus they have a scale of "1". 

I dropped 11 needles and got 7 hits.

So:  2 x needle unit 1 x 11 drops divided by 7 hits = 3.14285

2(1)(11)/7 = 3.14285

Pi is = 3.141592...




This was the first (and only) drop I did. By the way, if you take a ruler and continue the lines every 3/4" the 3 needles that fell towards the bottom wouldn't have hit any lines...had I bothered to draw them in. The lowest needle would have been close though.

Let's take that scenario:  2(1)(11)/8 = 2.75

Yeah, I'll fudge a little and keep my nice 7 hits instead of 8.

So, eventually when I post my RF and AF probe builds they'll probably have something about sine waves (which are 2 pi in proportion...I think).