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I am in economic, first day a novice in Monte Carlo even both, today my stranger friend give me a sample to finding pi area using Random Sample where area of circle divided by area of square

my question is:

  1. Why the sample should be and always use pi in the area of square of box. Could i change the pi function with supply and Demand function or any economic functions?

  2. If the the pi function in monte carlo always use box square as the exterior, Is it possible without the square to calculate the pi as interior?

time machine
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  • Since you haven't shown us what your "stranger friend" gave you, it's hard to know what you are talking about. It's also hard to know whether your friend was trying to explain something about "demand and supply", or just trying to give you an example of applying Monte Carlo methods to a math problem. Please edit your question so we can understand what exactly it is that you are asking. – Gerry Myerson Apr 10 '19 at 03:46
  • done sir @GerryMyerson – time machine Apr 10 '19 at 04:15
  • do you have any idea ?@GerryMyerson – time machine Apr 10 '19 at 04:16
  • I still don't think I understand the question at all. You keep on referring to "Monte Carlo", but you never say what you mean by that phrase. I think maybe you are referring to finding the area of a region $A$ by enclosing it in a region $B$ of known area, then generating a random collection of points inside $B$, and seeing how many of them are in $A$. If that's the case, then it should work with pretty nearly any set $A$ that's likely to come up in practice, whether it be a circle or some set coming from Economics. – Gerry Myerson Apr 10 '19 at 06:27

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I'm afraid I don't understand your first question fully, so I'll skip that. But as for your second, any shape with a known area is fine. You can use a 4657-gon for all it matters, as long as you know the area. Obviously, if you use a 4657-gon, you're gonna have a pretty hard time determining which points are in and out of the inside shape. Essentially, for your situation, if you can stick a circle in it, it's fine.

H Huang
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