A084660 Decimal expansion of solution of area bisectors problem.

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, 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, 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

Offset: 0

Author

Zak Seidov, Jun 28 2003

Keywords

• cons
• easy
• nonn

Examples

			0.0198603854199589820629240910936324260566251...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Henry Bottomley, Area bisectors of a triangle.
• Zak Seidov 3-points in 3-4-5 triangle

Programs

Magma

SetDefaultRealField(RealField(119)); Log(8/Exp(2))/4 // G. C. Greubel, Mar 22 2023

Mathematica

Join[{0}, RealDigits[N[3/4*Log[2]-1/2, 108]][[1]]] (* Georg Fischer, Jul 15 2021 *)

PARI

3*log(2)/4-1/2 \\ Charles R Greathouse IV, Apr 13 2020

SageMath

numerical_approx(log(8/exp(2))/4, digits=119) # G. C. Greubel, Mar 22 2023

Formula

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

Sum_{i>0} 1/((4i-1)*4i*(4i+1)) = Sum_{i>0} 1/A069140(i). - Henry Bottomley, Jul 09 2003

Extensions

a(100) corrected by Georg Fischer, Jul 15 2021