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Bertrand's paradox: a physical way out along the lines of Buffon's needle throwing experiment

Di Porto, P. and Crosignani, B. and Ciattoni, A. and Liu, H. C. (2011) Bertrand's paradox: a physical way out along the lines of Buffon's needle throwing experiment. European Journal of Physics, 32 (3). pp. 819-825. ISSN 0143-0807. https://resolver.caltech.edu/CaltechAUTHORS:20110506-111932532

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Abstract

Bertrand's paradox (Bertrand 1889 Calcul des Probabilités (Paris: Gauthier-Villars)) can be considered as a cautionary memento, to practitioners and students of probability calculus alike, of the possible ambiguous meaning of the term 'at random' when the sample space of events is continuous. It deals with the existence of different possible answers to the following question: what is the probability that a chord, drawn at random in a circle of radius R, is longer than the side R √3 of an inscribed equilateral triangle? Physics can help to remove the ambiguity by identifying an actual experiment, whose outcome is obviously unique and prescribes the physical variables to which the term 'random' can be correctly applied. In this paper, after briefly describing Bertrand's paradox, we associate it with an experiment, which is basically a variation of the famous Buffon's needle experiment (Buffon 1733 Histoire de l'Acad. Roy. des. Sciences pp 43–5; Buffon 1777 Histoire naturelle, générale et particulière Supplément 4 46) for estimating the value of π. Its outcome is compared with the analytic predictions of probability calculus, that is with the probability distribution of variables whose uniform distribution can be considered a sound implementation of complete randomness.


Item Type:Article
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http://dx.doi.org/10.1088/0143-0807/32/3/017DOIUNSPECIFIED
http://iopscience.iop.org/0143-0807/32/3/017/PublisherUNSPECIFIED
http://stacks.iop.org/EJP/32/819PublisherUNSPECIFIED
Additional Information:© 2011 IOP Publishing. Received 14 February 2011, in final form 11 March 2011. Published 12 April 2011.
Issue or Number:3
Classification Code:PACS: 01.40.-d; 02.50.Cw; 05.40.-a
Record Number:CaltechAUTHORS:20110506-111932532
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110506-111932532
Official Citation:Bertrand's paradox: a physical way out along the lines of Buffon's needle throwing experiment P Di Porto et al 2011 Eur. J. Phys. 32 819
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23575
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:09 May 2011 15:42
Last Modified:03 Oct 2019 02:47

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