Results
| Total Needles: | - |
| Line Crossings: | - |
| π Estimate: | - |
| True π: | - |
| Absolute Error: | - |
| Standard Error: | - |
Buffon’s Needle
probability
monte-carlo
visualization
Estimate the value of π using Buffon’s needle problem - a classic probability experiment that connects geometry with randomness.
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About This App
Buffon’s Needle is a classic problem in geometric probability, first posed by Georges-Louis Leclerc, Comte de Buffon, in the 18th century. The problem involves dropping needles on a floor made of parallel strips and counting how many needles cross the lines between the strips.
This simple physical experiment can be used to estimate π! The probability that a needle of length \(\ell\) will cross a line when dropped on a floor with parallel lines spaced \(d\) apart (where \(\ell \leq d\)) is:
\[P = \frac{2\ell}{\pi d}\]
By rearranging this formula and using the Law of Large Numbers, we can estimate π by performing many trials:
\[\pi \approx \frac{2\ell \cdot n}{d \cdot c}\]
where \(n\) is the total number of needles dropped and \(c\) is the number that cross a line.