𝜋 Generator (#2)

Jonathan Frech, 29 March 2015

Using Python and Pygame I created a program which approximates 𝜋. On the square screen points will randomly appear. Based on the distance to the center the points get a different color. Divided into two groups (the red points and the gray points) the program can roughly estimate 𝜋.

How it calculates

The red points represent the circle area. $A'=\pi\cdot r^2$ $A'=\pi\cdot r^2$
The gray points represent the square area minus the circle area. Thus the gray points and the red points the square area. $A''=\big(2\cdot r\big)^2=4\cdot r^2$ $A''=\big(2\cdot r\big)^2=4\cdot r^2$
We get $\frac{\pi}{4}$ $\frac{\pi}{4}$ , when we divide one by another. $\frac{A'}{A''}=\frac{\pi\cdot r^2}{4\cdot r^2}=\frac{\pi}{4}$ $\frac{A'}{A''}=\frac{\pi\cdot r^2}{4\cdot r^2}=\frac{\pi}{4}$
Lastly, we need to multiply by four to get 𝜋. $\frac{A'}{A''}\cdot 4=\pi$ $\frac{A'}{A''}\cdot 4=\pi$

Source code: pi-generator.py

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