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A195389 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(5),sqrt(7) right triangle ABC.

%I A195389 #12 Dec 24 2017 09:25:51
%S A195389 5,7,3,8,9,4,9,4,2,7,4,8,6,8,2,3,0,6,8,5,9,4,1,0,2,1,1,4,2,6,4,4,0,2,
%T A195389 2,8,6,9,3,9,8,0,8,1,9,5,3,5,4,9,9,1,1,5,0,5,7,5,2,0,9,5,2,0,9,2,4,5,
%U A195389 4,7,0,8,0,9,5,1,8,9,1,7,5,0,5,0,8,1,2,7,6,3,1,2,8,9,1,0,5,0,7,7
%N A195389 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(5),sqrt(7) right triangle ABC.
%C A195389 See A195284 for definitions and a general discussion.
%H A195389 G. C. Greubel, <a href="/A195389/b195389.txt">Table of n, a(n) for n = 0..10000</a>
%e A195389 Philo(ABC,I)=0.5738949427486823068594102114264402286939808...
%t A195389 a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];
%t A195389 f = 2 a*b/(a + b + c);
%t A195389 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195389 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195389 x3 = f*Sqrt[2]
%t A195389 N[x1, 100]
%t A195389 RealDigits[%]   (* (A) A195386 *)
%t A195389 N[x2, 100]
%t A195389 RealDigits[%]   (* (A) A195387 *)
%t A195389 N[x3, 100]
%t A195389 RealDigits[%]   (* (A) A195388 *)
%t A195389 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195389 RealDigits[%]   (* Philo(ABC,I) A195389 *)
%Y A195389 Cf. A195284, A195386, A195387, A195388.
%K A195389 nonn,cons
%O A195389 0,1
%A A195389 _Clark Kimberling_, Sep 17 2011