high School⏱ 5 min
Buffon's Needle
Estimating π by dropping needles on lines
○Not Started
crosses a lineno crossing
Needles per click
Needle length L = 0.80·d
Throws
0
Crossings
0
Crossing probability
0.0%
Estimated π
-
Actual π
3.14159
Error
-
Estimated π vs. throws
What is Buffon's Needle?
You randomly drop a needle of length L onto paper ruled with parallel lines spaced d apart, and count how many needles cross a line.
Why can it estimate π?
The chance of a crossing is 2L/(πd). Because π appears in it, we can solve for π from the ratio of throws to crossings.
Why does it get more accurate?
By the law of large numbers the crossing ratio approaches the true probability as throws grow, so the π estimate converges toward its real value.