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A115456 Decimal expansion of mean perimeter of a quadrilateral inscribed in a square of unit side. 0

%I

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

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

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

%N Decimal expansion of mean perimeter of a quadrilateral inscribed in a square of unit side.

%F Equals 4 * Integral_{x=0..1, y=0..1} sqrt(x^2 + y^2) = (4/3)*(sqrt(2) + arcsinh(1)).

%F Equals (4/3)*(sqrt(2)+log(sqrt(2)+1)) = 4/3*(sqrt(2)+arcsinh(1)).

%e 3.0607828658568507653790640655859871834637762715181...

%t RealDigits[N[(4/3)*(Sqrt[2] + ArcSinh[1]), 100]][[1]]

%o (PARI) (sqrt(2)+asinh(1))*4/3 \\ _Charles R Greathouse IV_, Jul 13 2015

%K cons,nonn

%O 1,1

%A _Zak Seidov_, May 07 2007

%E Typo in Mathematica program fixed by _Zak Seidov_, Nov 19 2011

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Last modified April 19 21:11 EDT 2021. Contains 343117 sequences. (Running on oeis4.)