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May, 1994 A Lewis Carroll Pillow Problem: Probability of an Obtuse Triangle
Stephen Portnoy
Statist. Sci. 9(2): 279-284 (May, 1994). DOI: 10.1214/ss/1177010497


On the 100th anniversary (1993) of Lewis Carroll's Pillow Problems, Eugene Seneta presented a selection of the problems the author, Charles Dodgson, claims to have solved while in bed. The selection omits the one problem in continuous probability: "Three points are taken at random on an infinite plane. Find the chance of their being the vertices of an obtuse-angled triangle." Charles Dodgson presents a solution that involves a clear error in conditioning. An alternative solution is suggested here. This solution seems rather natural and should be especially appealing to statisticians. The nature of the solution suggests a method for using transformation groups to give meaning to the phrase "at random" in somewhat general situations.


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Stephen Portnoy. "A Lewis Carroll Pillow Problem: Probability of an Obtuse Triangle." Statist. Sci. 9 (2) 279 - 284, May, 1994.


Published: May, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0955.60502
MathSciNet: MR1293297
Digital Object Identifier: 10.1214/ss/1177010497

Keywords: homogeneous space , invariant measure , Random triangle , sampling at random , transformation group

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.9 • No. 2 • May, 1994
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