A352484 Decimal expansion of the probability that when three real numbers are chosen at random, uniformly and independently in the interval [0,1], they can be the lengths of the sides of a triangle whose altitudes are also the sides of some triangle.
3, 0, 5, 8, 3, 6, 7, 2, 2, 2, 5, 0, 7, 8, 8, 8, 7, 5, 6, 3, 4, 3, 5, 9, 5, 8, 1, 7, 0, 1, 9, 7, 8, 1, 7, 2, 1, 6, 0, 3, 2, 2, 4, 2, 0, 1, 4, 3, 4, 2, 6, 6, 0, 6, 7, 8, 3, 8, 7, 5, 0, 5, 8, 6, 0, 1, 1, 9, 9, 0, 4, 5, 9, 0, 4, 0, 4, 3, 4, 3, 2, 6, 8, 0, 5, 0, 0, 5, 9, 1, 5, 5, 7, 9, 9, 9, 2, 8, 7, 6, 0, 4, 7, 8, 5
Offset: 0
Examples
0.30583672225078887563435958170197817216032242014342...
Links
- Mohammed Yaseen, Table of n, a(n) for n = 0..10000
- Murray S. Klamkin, Problem 1494, Crux Mathematicorum, Vol. 15, No. 10 (1989), p. 298; Solution to Problem 1494, by P. Penning, ibid., Vol. 17, No. 2 (1991), pp. 53-54.
- Eric Weisstein's World of Mathematics, Altitude.
- Index entries for transcendental numbers.
Programs
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Mathematica
RealDigits[2*Log[Sqrt[5] - 1] + 1 - Sqrt[5]/2, 10, 100][[1]]
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PARI
2*log(sqrt(5)-1) + 1 - sqrt(5)/2 \\ Charles R Greathouse IV, Nov 26 2024
Formula
Equals 2*log(sqrt(5)-1) + 1 - sqrt(5)/2.
Comments