Buffon's Needle

The Magic of $\pi$

If you drop a needle of length $l$ onto a floor with parallel lines spaced distance $d$ apart, the probability $P$ that the needle crosses a line is related to $\pi$.

When $l = d$, the math is beautiful:

$P = \frac{2}{\pi}$

By rearrangeing the formula, we can estimate $\pi$ using our drops:

$\pi \approx 2 \times \frac{\text{Total Drops}}{\text{Crosses}}$

I see!