Abstract
It has long been known that the Buffon needle experiment can be used to estimate π. This raises a question which we investigate in this paper, linking statistics and geometry: how should a grid be laid out in order to give a tight estimator of π? We study four grids: Buffon's single grid, Laplace's double grid, Uspensky's triple grid and the hexagonal tiling. We standardise the grids to have equal "grid density" and find that Buffon's single grid with the maximum length needle provides the tightest estimator of π, for the range of needle lengths studied.
| Original language | English |
|---|---|
| Pages (from-to) | 415-421 |
| Number of pages | 7 |
| Journal | Statistics and Probability Letters |
| Volume | 37 |
| Issue number | 4 |
| Publication status | Published - 30 Mar 1998 |
Keywords
- Asymptotic efficiency
- Asymptotic variance
- Buffon needle
- Grid density
- Information
- Regular tiling