Buffon's needle experiment consists of dropping a needle on hardwood floor, with floorboards of width 1. The experiment is shown graphically in the first graph box. The angle X of the needle relative to the floorboard cracks and the distance Y from the center of the needle to the lower crack are recorded in the first table on each update. Each point (X, Y) is shown as a red dot in the scatterplot. The variable I indicates the event that the needle crosses a crack.
The density of I is shown in blue in the distribution graph and is recorded in the distribution table. On each update, the empirical density of I is shown in red in the distribution graph and is also recorded in the distribution table. Finally, pi is shown in blue in the last graph and is recorded in the last table, and on each update, Buffon's estimate of pi is shown in red in the last graph and is recorded in the last table. The parameter is the needle length L, which can be varied with a scrollbar.

## Software/Applets used on this page

## Glossary

### density

the ratio of the mass of an object to its volume

### event

any set of possible outcomes of a statistical experiment

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### parameter

a) a constant or variable term in a function that determines the specific form of the function but not its general nature, as a in f(x) = ax, where a determines only the slope of the line described by f(x).

b) one of the independent variables in a set of parametric equations.

b) one of the independent variables in a set of parametric equations.

### pi

the ratio of the circumference of a circle to its diameter. It is approximately 3.14159265...

### variable

A value which is unknown and free to vary, often denoted by x or y.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

AQA AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

AQA AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

CBSE XII (India) | Probability | Probability | Repeated independent (Bernoulli) trials and binomial distribution | - |

CBSE XI (India) | Statistics and Probability | Probability | Random experiments, outcomes, sample spaces (set representation) | - |

CCEA A-Level (NI) | S1 | Probability | Experimental | - |

CIE A-Level (UK) | S1 | Probability | Experimental | - |

Edexcel A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

Edexcel AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

Edexcel AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

I.B. Higher Level | 5 | Probability | Experimental | - |

I.B. Standard Level | 5 | Probability | Experimental | - |

Methods (UK) | M15 | Probability | Experimental | - |

I.B. (MSSL) | 3 | Probability | Experimental | - |

OCR A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

OCR AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

OCR MEI AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

OCR-MEI A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

Pre-Calculus (US) | E4 | Probability | Experimental | - |

Pre-U A-Level (UK) | Prob | Probability | Experimental | - |

Scottish (Highers + Advanced) | HS | Probability | Experimental | - |

Scottish Highers | S | Probability | Experimental | - |

Universal (all site questions) | P | Probability | Experimental | - |

WJEC A-Level (Wales) | S1 | Probability | Experimental | - |