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Calculate π by Simulation

# patrickbucher/simulate-pi

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# Simulate Pi (π)

## Rationale

• A circle with radius `r` has the surface `r²π`.
• A circle with radius `r=1` has the surface `π`.
• A quarter of a circle with radius `r=1` has the surface `π/4`.
• A square with side length `s` has the surface `s²`.
• A square with side length `s=1` has the surface `1`.

Given a square with side length `s=1` containing a quarter circle with `r=1` and its center at a corner of the square: If a dot is drawn randomly on that square:

• The probability of the dot being drawn within the square is `P(S)=1`.
• The probability of the dot being drawn within the quarter circle is equal to the ratio of the circle area to the square area, i.e. `P(C)=(π/4)/1=π/4`.

If the ratio `P(C)/P(S)` of dots drawn onto the quarter circle to dots being drawn onto the square is `π/4`, then `π=4*P(C)/P(S)`.

Thus, `π` can be calculated by taking the ratio of the number of dots drawn within the circle and the number of dots totally drawn on the square, multiplied by four.

Calculate π by Simulation

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