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A195380 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(3),sqrt(1) right triangle ABC (angles 30, 60, 90).

%I A195380 #6 Mar 30 2012 18:57:45
%S A195380 5,5,7,5,7,0,1,7,6,9,1,7,0,9,3,8,0,3,7,2,1,1,2,9,1,4,6,0,4,2,9,2,3,1,
%T A195380 8,7,2,1,1,5,2,6,1,0,0,8,9,0,3,0,5,5,9,9,2,1,6,7,9,5,5,8,9,0,9,5,8,8,
%U A195380 2,5,6,8,1,9,4,3,6,5,6,9,3,1,0,6,8,1,8,1,7,7,7,1,2,4,7,7,1,9,3,5
%N A195380 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(3),sqrt(1) right triangle ABC (angles 30, 60, 90).
%C A195380 See A195284 for definitions and a general discussion.
%e A195380 Philo(ABC,I)=0.55757017691709380372112914604292318...
%t A195380 a = 1; b = Sqrt[3]; c = 2;
%t A195380 f = 2 a*b/(a + b + c);
%t A195380 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195380 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195380 x3 = f*Sqrt[2]
%t A195380 N[x1, 100]
%t A195380 RealDigits[%] (* (A) A195348 *)
%t A195380 N[x2, 100]
%t A195380 RealDigits[%] (* (B) A093821 *)
%t A195380 N[x3, 100]
%t A195380 RealDigits[%] (* (C) A120683 *)
%t A195380 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195380 RealDigits[%] (* A195380 *)
%Y A195380 Cf. A195284.
%K A195380 nonn,cons
%O A195380 0,1
%A A195380 _Clark Kimberling_, Sep 17 2011