It's Pi Day (in America), everyone's favorite mathematically-themed non-holiday and excuse to eat pie. So grab some ping pong balls and let's do an experiment! (From 2010)
I don't really want to set this up, so I am going to do it with a program instead. Here is a program that will generate random points in a 1 x 1 square.Now, here is the key. What if I calculate the distance of each of these point from the origin? This would simply be:
Doing this, I can separate all the points into those that are more than 1 unit away from the origin and those that are less than 1 unit away. In this plot, the red dots are more than one unit away and the blue are 1 unit or less. Note that this plot does not have exactly the same horizontal and vertical scale - no idea why it came out like that. However, this is enough dots that maybe you can see a pattern. The blue dots are filling up 1/4Since I am a physicist, I have trouble leaving the area as unitless.
Doing this for my last random number run, I get pi=3.04. What happens as I increase the number of random dots? This a plot of the estimation of Pi for numbers of dots starting at 1000 up to 100,000 dots. I did this 5 times because each time is different. So, you can see that as the number of random points increases, the estimated value of Pi is a little less spread out and closer to 3.14-something.
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