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(1) randomly plot points inside the unit square (2) some will fall within the unit circle The fraction of points inside the circle approaches π/4 as the number of points → ∞ (source: https://commons.wikimedia.org/wiki/File:Pi_30K.gif …)pic.twitter.com/7R08x6k3AN
Buffon's Needle Trick is my fav way of approximating π (1) draw parallel lines separated by the needles length (2) throw a bunch of needles in the air (& run) (3) the fraction of needles that cross a line → 2/π as # of needles → ∞ (source:http://mathgifs.blogspot.com/2013/11/buffons-needle-and-his-noodles.html …)pic.twitter.com/nlzbguepum
Here's an explanation for Buffon's Needle Trick I wrote a while back, for those curious.pic.twitter.com/CVjvckVkvp
whoa
Oooo, the Exploratorium has a physical version of this.https://www.exploratorium.edu/exhibits/pi-toss …
Have you ever seen the random walk methods for approximating π? It works in higher dimensions, toohttps://twitter.com/ajpizzuto/status/1106205442479411200?s=20 …
There' a good numberphile video where they explain why this is true - it has to do with the spacing being equal to the length of the needles and the possible angles that the needles can land at (i.e. the conditions for a miss)
Which method is faster?
Best ever rendition of the idea: A Ballistic Monte Carlo Approximation of Pi https://arxiv.org/abs/1404.1499
If, for some reason, I wanted this Buffon Needle sim to give a good result (i.e. fast convergence to 2/pi), would I want a circular problem topology? (i.e. add distances mod the top and bottom, semi-Pac-Man style)
(I would want this cuz then I need fewer needles to get fast convergence to high accuracy, assuming that wouldn’t cause problems)
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