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A075549
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Decimal expansion of 9 - 12*log(2).
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3
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6, 8, 2, 2, 3, 3, 8, 3, 3, 2, 8, 0, 6, 5, 6, 2, 8, 6, 9, 9, 3, 2, 1, 4, 5, 4, 2, 5, 0, 1, 8, 8, 1, 1, 8, 3, 0, 9, 3, 9, 9, 8, 3, 8, 7, 6, 7, 6, 9, 3, 6, 9, 5, 0, 5, 5, 1, 8, 3, 9, 8, 8, 6, 0, 7, 9, 2, 7, 6, 5, 3, 6, 3, 6, 3, 6, 6, 3, 4, 1, 2, 7, 2, 9, 6, 4, 0, 0, 7, 6, 0, 4, 2, 9, 7, 5, 7, 4, 9, 4, 9, 5, 9, 8
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OFFSET
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0,1
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COMMENTS
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Choose two numbers at random from the interval [0,1] (using a uniform distribution). This will give three subintervals of lengths a, b and c. What is the probability that there is a triangle with sides a, b and c? Given that a such a triangle exists, what is the probability that it is obtuse? Answer: Probability that there is a triangle is 1/4. Probability for this triangle to be obtuse is = 9 - 12 * log(2) = 0.68223... .
The problem proposed by Singmaster (1973) is to the calculate the probability that the three segments can form an obtuse triangle. Its solution is 1/4 of this constant, i.e., 9/4 - 3*log(2) = 0.170558... . - Amiram Eldar, May 20 2023
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REFERENCES
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Paul J. Nahin, Digital Dice: Computational Solutions to Practical Probability Problems, Princeton University Press, 2008, pp. 31-32.
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LINKS
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David Singmaster, Problem 858, Mathematics Magazine, Vol. 46, No. 1 (1973), p. 43; Probability of an Obtuse Triangle, Solution to Problem 85 by Major G. C. Holterman, ibid., Vol. 46, No. 5 (1973), pp. 294-295.
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EXAMPLE
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0.682233833280656286993214542501881183...
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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