Buffon’s needle problem
E636452
Buffon’s needle problem is a classic probability puzzle that involves dropping a needle on a lined surface to estimate the value of π.
Observed surface forms (5)
| Surface form | Occurrences |
|---|---|
| Buffon's law | 1 |
| Buffon's needle | 1 |
| Buffon's needle problem | 1 |
| Buffon’s needle experiment | 1 |
| probabilistic method known as Buffon's needle | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
Monte Carlo method example
ⓘ
geometric probability problem ⓘ probability puzzle ⓘ |
| appearsIn |
Monte Carlo methods courses
ⓘ
introductory probability textbooks ⓘ |
| assumes |
independent trials for each needle drop
ⓘ
needle is dropped with random position and orientation ⓘ parallel lines are equally spaced ⓘ |
| canEstimate | π ≈ 2L·(number of drops) / (T·number of crossings) ⓘ |
| category |
classical probability problem
ⓘ
stochastic simulation example ⓘ |
| demonstrates |
connection between geometry and probability
ⓘ
law of large numbers ⓘ |
| field |
geometric probability
ⓘ
mathematics ⓘ probability theory NERFINISHED ⓘ |
| hasAlternativeFormulation |
dropping a stick on floorboards
ⓘ
throwing a needle on ruled paper ⓘ |
| hasCondition | needle length less than or equal to line spacing ⓘ |
| hasFormula | P(cross) = 2L / (πT) for L ≤ T ⓘ |
| hasGeneralization |
Buffon–Laplace needle problem
NERFINISHED
ⓘ
problems with needle length greater than line spacing ⓘ |
| hasOutcome | probability depends on ratio L/T ⓘ |
| hasParameter |
distance between parallel lines
ⓘ
needle length ⓘ |
| historicalPeriod | 18th century ⓘ |
| introducedBy | Georges-Louis Leclerc, Comte de Buffon NERFINISHED ⓘ |
| involves |
dropping a needle onto a plane with parallel lines
ⓘ
estimating the probability of the needle crossing a line ⓘ |
| isTaughtIn |
courses on stochastic simulation
ⓘ
undergraduate probability courses ⓘ |
| namedAfter | Georges-Louis Leclerc, Comte de Buffon NERFINISHED ⓘ |
| relatedTo |
Buffon’s noodle problem
NERFINISHED
ⓘ
Monte Carlo integration NERFINISHED ⓘ estimation of irrational constants ⓘ geometric probability integral ⓘ |
| requires |
uniform distribution of needle angle
ⓘ
uniform distribution of needle center position ⓘ |
| solutionInvolves |
integration over angle and distance
ⓘ
trigonometric functions ⓘ |
| symbolUses |
L for needle length
ⓘ
T for distance between lines ⓘ π for pi ⓘ |
| usedFor |
demonstrating experimental probability
ⓘ
estimating the value of π ⓘ illustrating Monte Carlo estimation ⓘ |
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Georges-Louis Leclerc, Comte de Buffon
this entity surface form:
Buffon's needle
subject surface form:
Georges-Louis Leclerc, Comte de Buffon
this entity surface form:
Buffon's law
subject surface form:
Georges-Louis Leclerc, Comte de Buffon
this entity surface form:
Buffon's needle problem
subject surface form:
Georges-Louis Leclerc, Comte de Buffon
this entity surface form:
probabilistic method known as Buffon's needle