A352485 - OEIS

%I #9 Apr 26 2022 20:54:01

%S 2,3,2,9,8,1,4,5,8,3,1,3,6,0,9,6,9,3,3,3,4,6,3,9,7,5,9,0,8,1,4,5,3,0,

%T 2,1,0,1,8,9,6,9,6,3,8,0,9,6,6,9,5,1,7,1,4,1,6,8,1,4,6,4,9,5,8,2,1,4,

%U 6,9,1,7,1,0,6,7,1,6,7,0,7,2,6,7,5,7,6,6,3,5,2,7,3,3,2,7,8,9,2,9,7,5,1,9,3

%N Decimal expansion of the probability that when a unit interval is broken at two points uniformly and independently chosen at random along its length the lengths of the resulting three intervals are the altitudes of a triangle.

%H Mohammed Yaseen, <a href="/A352485/b352485.txt">Table of n, a(n) for n = 0..10000</a>

%H Eugen J. Ionascu, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.08.699">Problem 11663</a>, The American Mathematical Monthly, Vol. 119, No. 8 (2012), pp. 699-706; <a href="https://home.gwu.edu/~maxal/P11666.pdf">alternative link</a>; <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.121.08.738">Are Random Breaks the Altitudes of a Triangle?</a>, Solution to Problem 116633, by David Farnsworth and James Marento, ibid., Vol. 121, No. 8 (2014), pp. 741-743.

%H Eugen J. Ionaşcu and Gabriel Prăjitură, <a href="https://csuepress.columbusstate.edu/bibliography_faculty/1167/">Things to do with a broken stick</a>, International Journal of Geometry, Vol. 2, No. 2 (2013), pp. 5-30; <a href="https://arxiv.org/abs/1009.0890">arXiv preprint</a>, arXiv:1009.0890 [math.HO], 2010-2013.

%H Roberto Tauraso, <a href="https://www.mat.uniroma2.it/~tauraso/AMM/AMM11663.pdf">Problem 11663</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Altitude.html">Altitude</a>.

%F Equals 12*sqrt(5)*log((3+sqrt(5))/2)/25 - 4/5.

%F Equals 24*sqrt(5)*log(phi)/25 - 4/5, where phi is the golden ratio (A001622).

%e 0.23298145831360969333463975908145302101896963809669...

%t RealDigits[24*Sqrt[5]*Log[GoldenRatio]/25 - 4/5, 10, 100][[1]]

%Y Cf. A001622, A002390.

%Y Similar sequences: A016627, A019702, A084623, A243398, A339392, A339393, A352484.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 18 2022