3 ms·

"But computing pi is one of the worst possible illustrations of why anyone would use Monte Carlo, because it's inferior to the naive approach. i.e., it doesn't

"But computing pi is one of the worst possible illustrations of why anyone would use Monte Carlo, because it's inferior to the naive approach. i.e., it doesn't motivate why anyone would want to use Monte Carlo." Any suggestions for a simulation that does illustrate the use of Monte Carlo methods while still being explainable with 16+ age range non-specialist mathematics? I'm hacking around with two step simulations like a tree diagram... http://sohcahtoa.org.uk/pages/maths_montecarlo.html http://sohcahtoa.org.uk/pages/maths_montecarlo.html My crack at saying how slowly a monte-carlo simulation 'converges' to a value of pi (not really converging, just confidence intervals tightening around the value).

jwmerrill 12y ago
I like computing the volume of the intersection of 3 orthogonal cylinders as a less trivial example problem. It's still easy to compute whether a given point is inside the volume, and there's still an analytic solution to compare to, but the problem is complicated enough that you start to appreciate how much easier MC is than other approaches.
- jwmerrill 12y ago
  Or compute the area of the mandlebrot set. This one has the advantage of being highly non-convex, which makes it hard to decide how to implement a recursive subdivision routine, since you don't know whether some of the target area is inside a given square just from looking at a few points on its boundary.
  - keithpeter 12y ago
    Mandlebrot set a bit over the maths level for intended group, but other repeated maps like logistic equation might be OK. I'll go with the cylinders first!
- keithpeter 12y ago
  Sounds nice. Easy to visualise and close enough to a crucible design (toroidal volume intersected by a cube off axis and oblique to the central axis of the toroid) I once heard of in the days of Fortran.
wfunction 12y ago
Yeah, search for "Example #1" and subsequently "Monte Carlo" on this page: http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/ http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bay...

jwmerrill 12y ago

I like computing the volume of the intersection of 3 orthogonal cylinders as a less trivial example problem. It's still easy to compute whether a given point is inside the volume, and there's still an analytic solution to compare to, but the problem is complicated enough that you start to appreciate how much easier MC is than other approaches.

jwmerrill 12y ago
Or compute the area of the mandlebrot set. This one has the advantage of being highly non-convex, which makes it hard to decide how to implement a recursive subdivision routine, since you don't know whether some of the target area is inside a given square just from looking at a few points on its boundary.
- keithpeter 12y ago
  Mandlebrot set a bit over the maths level for intended group, but other repeated maps like logistic equation might be OK. I'll go with the cylinders first!
keithpeter 12y ago
Sounds nice. Easy to visualise and close enough to a crucible design (toroidal volume intersected by a cube off axis and oblique to the central axis of the toroid) I once heard of in the days of Fortran.

wfunction 12y ago

Yeah, search for "Example #1" and subsequently "Monte Carlo" on this page: http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/ http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bay...