Dots
.
Dots In
Circle
.

pi Approximation #2

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

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.

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?