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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
Implemented this some time ago. Integrals, too, suffer from the curse of dimensionality. A great and easy way to solve these problems is to use Monte Carlo integration!pic.twitter.com/qYikFCc6kw
i prefer the name "integration by darts" ;)
Draw quasi-random numbers instead and it will converge even faster.
and importance sample!
MS Excel to plot random points inside a circle. This is classic Monte Carlo simulation!
Converge here has to be in the probabilistic sense, otherwise there is no convergence.
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