Buffon got it straight

G. R. Wood*, J. M. Robertson

*Corresponding author for this work

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)415-421
    Number of pages7
    JournalStatistics and Probability Letters
    Volume37
    Issue number4
    Publication statusPublished - 30 Mar 1998

    Keywords

    • Asymptotic efficiency
    • Asymptotic variance
    • Buffon needle
    • Grid density
    • Information
    • Regular tiling

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  • Cite this

    Wood, G. R., & Robertson, J. M. (1998). Buffon got it straight. Statistics and Probability Letters, 37(4), 415-421.