Pi is an infinitely long decimal number that is never repeated. How will we know? Well, humans have calculated it to 314 trillion decimal places and not reached the end. At that time, I was willing to accept it. I mean, NASA only uses the first 15 decimal places to navigate spacecraft, and that’s more than enough for mundane applications.
The best part for me is that there are many ways to estimate that value, which I have written about before. For example, you can do this by oscillating a mass on a spring. But perhaps the strangest method of all was perfected by Georges Louis Leclerc, Comte de Buffon in 1777.
Decades ago, Buffon posed this as a probability question in geometry: Imagine you have a floor with parallel lines at a distance D. On this floor, you drop a bunch of needles lengthwise l. What is the probability that a needle will cross one of the parallel lines?
A picture will help you understand what is happening. Let’s say I only drop two needles on the floor (feel free to replace the needles with something safe like toothpicks). Also, to make things easier later, we can say that the length of the needle and the distance between the lines are equal to (D = L).
You may notice that one needle crosses one line and the other does not. OK, but what are the chances? This is not the most trivial problem, but let’s just think about a dropped needle. We only care about two values – distance (x) to a line from the far end of the needle, and the angle of the needle (θ) with respect to a perpendicular (see figure below). If x With less than half the distance between the lines, we get a needle-crossing. As you can see, you will get more probability with less probability x or small θ.
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