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A195372 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(2),sqrt(3) right triangle ABC.

%I A195372 #10 Dec 24 2017 09:25:42
%S A195372 5,9,0,5,6,8,0,8,0,0,1,5,9,9,7,1,3,4,3,7,4,7,0,4,6,4,4,1,6,4,6,5,0,5,
%T A195372 6,6,9,4,4,1,0,3,2,9,4,1,9,3,4,2,2,8,8,8,7,8,2,6,1,4,8,0,1,3,7,9,5,6,
%U A195372 6,0,0,7,2,4,2,4,6,8,5,7,1,9,9,1,0,8,4,5,3,9,5,3,6,8,5,5,6,5,0,7
%N A195372 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(2),sqrt(3) right triangle ABC.
%C A195372 See A195284 for definitions and a general discussion.
%H A195372 G. C. Greubel, <a href="/A195372/b195372.txt">Table of n, a(n) for n = 0..10000</a>
%e A195372 Philo(ABC,I)=0.590568080015997134374704644164650566944103294...
%t A195372 a = 1; b = Sqrt[2]; c = Sqrt[3];
%t A195372 f = 2 a*b/(a + b + c);
%t A195372 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195372 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195372 x3 = f*Sqrt[2]
%t A195372 N[x1, 100]
%t A195372 RealDigits[%]    (* (A) A195369 *)
%t A195372 N[x2, 100]
%t A195372 RealDigits[%]    (* (B) A195370 *)
%t A195372 N[x3, 100]
%t A195372 RealDigits[%]    (* (C) A195371 *)
%t A195372 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195372 RealDigits[%]    (* Philo(ABC,I) A195372 *)
%Y A195372 Cf. A195284, A195369, A195370, A195371.
%K A195372 nonn,cons
%O A195372 0,1
%A A195372 _Clark Kimberling_, Sep 17 2011