Showing posts with label Boffon's needle. Show all posts
Showing posts with label Boffon's needle. Show all posts

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).