Just wanted to share a fascinating little gem of maths that's been hiding in plain sight from us all along. Let's see how geometry itself is embedded in pure randomness!

The experimental setup is quite simple. All you need is something flat and grid-like (a tile floor for instance) and a thin "stick" of material cut to exactly half the width of the squares of our grid. You might want to have a pencil and paper or smartphone handy for calculations too.

Now all there is to do is toss our "stick" in the air and let it land on the grid. Be sure to keep count of the total number T of tosses. So if it lands on any of the horizontal lines of the grid then we simply add 1 to a counter C. (You could instead choose vertical line crossings by convention of course).

Repeat as many times as possible, the more the better. Once you've run a good number of trials you can begin to see the magic emerge. Divide the total T by the number of crossings C and what do you get? It should be a number very close to 3. In fact, as the number of trials increases, you should notice this ratio approach a very special number indeed: 3.1415926(...). That's right, it's Pi!

Okay so as I mentioned earlier, the accuracy of the result is strictly dependent upon the number of trials T, so the best approach here is to spread out the experiment over a number of days if possible. It can even be conducted continuously...provided one has the patience to do such a thing of course. But (filtering fluctuations aside) if you did you would get an increasingly more accurate approximation of the famous circle constant. (To be sure the ACTUAL circle constant is Tau, or twice Pi, but we won't get into that here!)

For reference: Buffon's Needle Problem.

The experimental setup is quite simple. All you need is something flat and grid-like (a tile floor for instance) and a thin "stick" of material cut to exactly half the width of the squares of our grid. You might want to have a pencil and paper or smartphone handy for calculations too.

Now all there is to do is toss our "stick" in the air and let it land on the grid. Be sure to keep count of the total number T of tosses. So if it lands on any of the horizontal lines of the grid then we simply add 1 to a counter C. (You could instead choose vertical line crossings by convention of course).

Repeat as many times as possible, the more the better. Once you've run a good number of trials you can begin to see the magic emerge. Divide the total T by the number of crossings C and what do you get? It should be a number very close to 3. In fact, as the number of trials increases, you should notice this ratio approach a very special number indeed: 3.1415926(...). That's right, it's Pi!

Okay so as I mentioned earlier, the accuracy of the result is strictly dependent upon the number of trials T, so the best approach here is to spread out the experiment over a number of days if possible. It can even be conducted continuously...provided one has the patience to do such a thing of course. But (filtering fluctuations aside) if you did you would get an increasingly more accurate approximation of the famous circle constant. (To be sure the ACTUAL circle constant is Tau, or twice Pi, but we won't get into that here!)

For reference: Buffon's Needle Problem.

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