Common area of circles

Gerard Flanagan grflanagan at
Thu Feb 4 18:24:37 CET 2010

Gary Herron wrote:
> Gerard Flanagan wrote:
>> A brute force approach - create a grid of small squares and calculate 
>> which squares are in all circles. I don't know whether it is any 
>> better than monte-carlo: 
> That's just what the monte-carlo method is -- except the full family of 
> monte-carlo methods can be quite sophisticated, including being more 
> general (pseudo or quasi random points instead of a regular grid) and 
> can provide a theoretical basis for calculating the rate of convergence, 
> and so on.

I would have said a Monte Carlo method necessarily involves random 
sampling in some shape or form, no? (Casinos, Chance etc..) And as I've 
previously understood Monte Carlo Integration, the technique involves 
rather the ratio "hits/total sample" rather than the sum of small areas. 
That's how I remember it, at least - it's been a while though.



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