Happy Approximately Pi Day, March 22

by alejandroerickson

55504

Intro: Happy Approximately Pi Day, March 22

This is a little late for pi day, but March 22nd is the perfect day to post this approximation of Pi.  The man behind the calculation is Comte de Buffon, 1707-1788.

To try this yourself you'll need a large-ish flat surface with parallel lines at regular intervals (same distances between them), and you'll need a needle or a straight stick.  It helps to have someone else write down the results so you can do your trials more quickly.

Drop the needle onto the lined surface so that it falls "randomly", and note whether it comes to rest on a line or not.  You'll get more "randomness" if you drop from higher up or toss the needle haphazardly.

Once you have done at least 100 trials, the formula for approximating Pi is... (twice the number of trials)/(number of times the needle crossed a line).  The more trials you do, the better your approximation will be!

My only question is... What do I eat on approximately π day?!? Apple crisp?

(picture in public domain, from wikipedia)


4 Comments

copperaxe 12 years ago

I never came across this method before. Having seen the experiment, your results and trying this on my own hardwood floors... I'm stumped how anyone came across this as a method of formulating Pi, let alone how the math applies in practical application. Use of geometry makes more sense. This seems like a way to find out how much rocket fuel is used to travel to Jupiter by counting the number of steps a horse takes due north before turning east and dividing it by the horses weight times the number of corn kernels that can fit in the bed of a Ford F-150 pickup. I don't doubt that it works, but how?

alejandroerickson 12 years ago

Haha, I like your analogy. It is not quite that far off though. You might come up with it starting with this: If I drop a needle on the floor boards and it falls at a certain spot, the positions in which it will touch a line are some fraction of a circle, specifically, a couple of pie slices (no pun intended). So it is conceivable that fractions of the circle have something to do with pi!  Here is wikipedia's diagram of what I described.  Needles which fall with their center at point x will cross the vertical line if they are in the shaded area.



Tanmay Das 12 years ago

Sorry brother but it's actually "Comte de Buffon" not "Compte Buffon".
Please correct that.