Buffon’s Needle

π from falling needles

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Buffon's needle (length = spacing) crosses a line with probability $2/\pi$.
• Dropping needles gives an estimate of $\pi$.
• The $\pi$ comes from averaging over all needle angles.
• Any curve of length ℓ averages 2ℓ/(πt) crossings: Buffon’s noodle.

Steps

1. An 18th-century puzzle
2. Drop needles
3. A shorter needle
4. An experiment
5. Too good to be true
6. Buffon’s noodle
7. Why π shows up