Dots

.

Dots In
Circle

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pi Approximation #2

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Current x

.

Current x coordinate of dot
Current y

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Current y coordinate of dot
x2 + y2

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(dot radius)2 = x2 + y2
Inside Circle?

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(dot radius)2 < 12 ?
Official pi

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Textbook value of pi
Estimated pi

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(Dots In Circle) / Dots x 4
Error

    .

(Official pi) - (Estimated pi)
Error Percent

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Error / (Official pi) x 100

Size of sampling grid

     


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.