0

How do you use a Monte Carlo method to approximate the area enclosed by the circle.

Nicholas Hausler
  • 23
  • 5
  • Did you see these items https://mathematica.stackexchange.com/questions/37074/finding-the-area-of-a-circle-using-monte-carlo-simulation and https://mathematica.stackexchange.com/questions/35683/finding-the-volume-of-a-sphere-using-the-monte-carlo-algorithm? – Moo Sep 12 '19 at 01:40

2 Answers2

3

Literally the Monte Carlo Method:

reg = RegionIntersection[Disk[], Disk[{1, 1}, 2]];
NIntegrate[1, {x, y} \[Element] reg, Method -> "MonteCarlo"]
(*  2.59499  *)
Michael E2
  • 235,386
  • 17
  • 334
  • 747
2
rndPts = Table[RandomReal[{-3, 3}],{10^6},{2}];
9 Length[Select[
    rndPts, #[[1]]^2 + #[[2]]^2 > 
       1 && (#[[1]] - 1)^2 + (#[[2]] - 1)^2 < 4 &]]/Length[rndPts]

2.51295

enter image description here

David G. Stork
  • 41,180
  • 3
  • 34
  • 96