# Buffon's Needle

## Theorem

Let a horizontal plane be divided into strips by a series of parallel lines a fixed distance apart, like floorboards.

Let a needle whose length equals the distance between the parallel lines be dropped onto the plane randomly from a random height.

Then the probability that the needle falls across one of the parallel lines is $\dfrac 2 \pi$.

## Proof

## Source of Name

This entry was named for Georges Louis Leclerc, Comte de Buffon.

## Historical Note

Augustus De Morgan reports that a pupil of his once performed a practical experiment using Buffon's Needle to calculate a value for $\pi$.

After $600$ trials, a value of $3.167$ was obtained.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$