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The Problem of the Thrown String

Published online by Cambridge University Press:  03 November 2016

J. L. Synge
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Extract

Some time ago I asked what is the average rectilinear distance D between the ends of a string of length L when thrown down at random on a table (The Mathematical Gazette, LII (1968) 165). I have to thank a number of correspondents (J. Clemow, R. 0. Davies, A. R. Everett, M. Fine, J. R. Hunt, G. S. Light and E. Sike) for letters about the problem. Some offered solutions based on simple assumptions regarding randomness. The simplest (Everett) is that all values of D in the range (0, L) are equally probable, and so the answer is \L. I do not find this assumption acceptable, nor the other assumptions put forward.

Type
Research Article
Information
The Mathematical Gazette , Volume 54 , Issue 389 , October 1970 , pp. 250 - 260
Copyright
Copyright © Mathematical Association 1970

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