Estimating Pi with the Digits of Pi //
If you enjoyed this video on pi, I think you'll also like my recent video on intransitive dice: • How Probability Helps Us Understand an Unb... . Thanks for watching!
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I put together a little visual estimating the value of pi using the digits of pi in a modified Monte Carlo kind of set up. If you'd like to play with the original @Desmos graph, you can see that here: https://www.desmos.com/calculator/ohm....
I say "modified" because of course the whole point of an actual Monte Carlo simulation is to choose the points at random, and then check if they lie within a particular area. In this case, the area is a circle inscribed inside of a square. The ratio of the area of the circle to the area of the square is π/4, so by multiplying the proportion of red points to all points by 4, we should get a decent estimate of pi.
Of course, "decent" is in the eye of the beholder. In this case, 10,000 points gets us within about half a percent of pi's actual value, which is good, but doesn't look all that impressive (i.e., it will sometimes start 3.14, but other times 3.13 or even 3.15). If you'd like to see the different values the Monte Carlo simulation can deliver, you can check out this graph: https://www.desmos.com/calculator/i4d....
Happy Pi Day 2023!
For more Pi Day fun, check out the pi-themed sudoku: • A Pi Sudoku Puzzle (for Pi Day!)
#piday2023 #piday #montecarlo
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