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A245698 Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to its center: (2*sqrt(3) + log(2+sqrt(3)))/18. 1

%I #12 May 15 2019 11:38:10

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

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

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

%N Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to its center: (2*sqrt(3) + log(2+sqrt(3)))/18.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Also equal to (8*sqrt(3)+3*arcsinh(sqrt(3))+log(2+sqrt(3)))/72.

%e 0.265614417336809516426663279462206287661810693282682096437...

%t RealDigits[(2Sqrt[3]+Log[2+Sqrt[3]])/18,10,120][[1]] (* _Harvey P. Dale_, Aug 09 2014 *)

%o (PARI) sqrt(3)/9 + log(sqrt(3)+2)/18 \\ _Charles R Greathouse IV_, May 15 2019

%Y Cf. A103712.

%K nonn,cons

%O 1,1

%A _Derek Orr_, Jul 29 2014

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)