Dots	.	Dots In Circle	.

pi Approximation Computer Simulation - Digital Sampling

Current x	.	Current x coordinate of dot
Current y	.	Current y coordinate of dot
x2 + y2	.	(dot radius)2 = x2 + y2
Inside Circle?	.	(dot radius)2 < 12 ?
Official pi	.	Textbook value of pi
Estimated pi	.	(Dots In Circle) / Dots x 4
Error	.	(Official pi) - (Estimated pi)
Error Percent	.	Error / (Official pi) x 100

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Size of sampling grid
10 x 10 100 x 100 1,000 x 1,000 10,000 x 10,000 100,000 x 100,000 1,000,000 x 1,000,000

Numerical approximation of pi using digital sampling.

Similar to the first pi approximation, only instead of random x and y coordinates, a regular grid of coordinates is used.

The larger the number of dots, the finer the grid (something like the pixel resolution of a digital camera), and the more accurate the approximation.

Compare with the Monte Carlo Method.

• For a given number of tries, which method gives a more accurate result?
• Does this change depending on the number of tries?
• Which method is more practical to use, if a large number of computers (with greatly varying speeds) are to be coordinated to together estimate the value of pi?