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Thursday, 18 November 2004



The circle-inside-a-square was used in one of my favourite classes ever at university.

-Take a random number generator that gives numbers between 0 and 1 inclusive with as much precision as you like (the more the better though)
-Ask for two random numbers. Assign them to an (X,Y) coordinate. Ex: (0.75488, 0.17340)
-Now imagine a square going from (0,0) to (1,1). All of your randomly generated coordinates must fall within this square.
-Now imagine a circle with a centre at (0.5,0.5) with a radius of 0.5. This circle is inscribed within the square. Not all of the random coords will fall within this circle.
-You can now establish that:
(# of points in circle)/(# of points in square) =
(area of circle)/(area of square)

-You know the ratio of Circle Area to Square Area = Pi /4
-Thus, 4* percent of points in the circle gives you a value of Pi.

Using only random numbers between 0 to 1, you can get a very good value for Pi! Crazy! The longer you let it run and/or the better the precision of your random numbers, the better your estimate of Pi.


Math geeks! I'ma skeered. I'ma haid unnerneatha this here table 'til youse guys er dun.

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