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Decimal expansion of solution of area bisectors problem.
1

%I #27 Mar 22 2023 08:07:22

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

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

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

%N Decimal expansion of solution of area bisectors problem.

%H G. C. Greubel, <a href="/A084660/b084660.txt">Table of n, a(n) for n = 0..10000</a>

%H Henry Bottomley, <a href="http://www.se16.info/js/halfarea.htm">Area bisectors of a triangle</a>.

%H Zak Seidov <a href="http://web.archive.org/web/20090902225120/http://geocities.com/zseidov/3points345.html">3-points in 3-4-5 triangle</a>

%F Equals (3*log(2) - 2)/4.

%F Sum_{i>0} 1/((4i-1)*4i*(4i+1)) = Sum_{i>0} 1/A069140(i). - _Henry Bottomley_, Jul 09 2003

%e 0.0198603854199589820629240910936324260566251...

%t Join[{0}, RealDigits[N[3/4*Log[2]-1/2, 108]][[1]]] (* _Georg Fischer_, Jul 15 2021 *)

%o (PARI) 3*log(2)/4-1/2 \\ _Charles R Greathouse IV_, Apr 13 2020

%o (Magma) SetDefaultRealField(RealField(119)); Log(8/Exp(2))/4 // _G. C. Greubel_, Mar 22 2023

%o (SageMath) numerical_approx(log(8/exp(2))/4, digits=119) # _G. C. Greubel_, Mar 22 2023

%K cons,easy,nonn

%O 0,3

%A _Zak Seidov_, Jun 28 2003

%E a(100) corrected by _Georg Fischer_, Jul 15 2021