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Uniform distributions and random triangles

Published online by Cambridge University Press:  22 September 2016

David Griffiths
David Griffiths*
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, P.O. Box 218, Lindfield, N.S.W., Australia 2070, currently at Faculty of Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA
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Extract

“What is the probability that a randomly drawn triangle is acute-angled?” This question has been discussed in recent Gazettes (for example by Trevor Easingwood in [2], followed up by Stephen Ainley in [1]). As Easingwood pointed out, the answer to this question depends on what properties of triangles are assumed to be random and on what one means by random. And as Ainley pointed out some of these assumptions can lead to a contradiction. A statistical model is necessary to define the sense in which the chosen properties (lengths of sides, angles, co-ordinates of vertices,…) are assumed random. This model may (and preferably will) relate to a possible physical ‘random’ mechanism for generating the random triangle.

Type
Research Article
Information
The Mathematical Gazette , Volume 67 , Issue 439 , March 1983 , pp. 38 - 42
Copyright
Copyright © Mathematical Association 1983 

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References

1. Ainley, E. S., A probable paradox. Math. Gaz. 66, 300–301 (1982).10.2307/3615519Google Scholar
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