🍕 Throw Pizza, Make Pi!

What's Going On?

We have a square, with a circle drawn inside it where the circle touches the sides of the square. If the sides of the square have the length 2, then the radius of the circle inside is 1. The formula for the area of a square is $\mathrm{area}=l^2$ where $l$ is the length of the sides of the square. The formula for the area of a circle is $\mathrm{area}=\mathrm{\pi }{r}^2$ where $r$ is the radius the circle.

Using our square and circle above, the area for the square is $2^2=4$ and the area for the circle is $\mathrm{\pi }\times 1^2=\mathrm{\pi }$

As we randomly throw pizza, it will always land in the area of the square, but will only sometimes land inside the circle. We can compare the number of slices thrown and the number of slices inside the pizza, and the ratio will be $\frac{\mathrm{circle\; hits}}{\mathrm{square\; hits}}\approx \frac{\mathrm{\pi }}{4}$ which we can multiply by 4 to get an estimate of Pi! The more slices we throw, the closer our estimate will be.

Happy Pi Day!