Introduction
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Although Pi is officially defined by the circumference of a circle, it is closely linked to a circle's area. A circle's area is given by A = πr^2 (also the integral of circumference C = 2πr). Therefore, knowing the area and radius of a circle can be used to approximate Pi. The radius is the easy part: any circle can be drawn with any chosen radius. The area is where the approximation comes in: by plotting random points on a circle inscribed in a square, the ratio of the circle's area to the square's area can be determined. Since we know the square's area is (2r)^2, the area of the circle can be approximated. The more random points generated, the better the approximation of pi. This is called the Monte Carlo Method.
Check out this Interactive Example! |
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With the radius of the circle set at 1, the area of the circle simply equals π.
Automation Procedure
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This problem is easier by only looking at one forth of a circle of radius 1. Now, points are generated by a random x and y value between 0 and 1.
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