Buffon's Needle π Estimation

Drop needles onto a wooden floor with parallel cracks to estimate π! This classic 1777 experiment by Georges-Louis Leclerc, Comte de Buffon, demonstrates how random sampling can compute deterministic mathematical constants.

P(crossing) = 2ℓ / (πd)

Therefore: π ≈ 2ℓn / (dk) where k = crossings out of n drops

✓ Valid when ℓ ≤ d (enforced by slider)

Crossing

Not Crossing

π Estimation Convergence

π ≈ —

Error: —

Needle Length (ℓ) ≤ d

ℓ = 1.6

Plank Width (d)

d = 1.6

Needles per Drop

100

Total Needles

Crossings

0.0%

Observed Rate

—

Theoretical Rate

—

Std Error (π̂)