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

0,1

Comments

Without the condition on the altitudes the probability is 1/2.

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.

Formula

Equals 2*log(sqrt(5)-1) + 1 - sqrt(5)/2.

Example

0.30583672225078887563435958170197817216032242014342...

Mathematica

RealDigits[2*Log[Sqrt[5] - 1] + 1 - Sqrt[5]/2, 10, 100][[1]]

Prog

(PARI) 2*log(sqrt(5)-1) + 1 - sqrt(5)/2 \\ Charles R Greathouse IV, Nov 26 2024

Crossrefs

Cf. A020837, A134972, A352485.

Sequence in context: A061035 A225233 A021331 * A013673 A188639 A103229

Adjacent sequences: A352481 A352482 A352483 * A352485 A352486 A352487

Keyword

nonn,cons

Author

Amiram Eldar, Mar 18 2022

Status

approved