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A195385 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,sqrt(5),3 right triangle ABC.

%I A195385 #7 Jul 18 2021 05:42:00
%S A195385 6,1,1,5,5,8,3,5,1,2,7,9,6,6,4,1,3,0,6,5,6,7,7,9,3,2,2,4,2,8,8,4,4,3,
%T A195385 2,7,0,7,7,7,0,6,7,2,5,0,0,1,8,5,3,0,9,3,1,9,2,6,0,2,3,8,0,2,9,1,7,4,
%U A195385 6,7,0,8,6,0,9,1,9,8,1,4,4,8,1,2,6,1,1,2,9,5,1,3,1,2,6,9,9,1,5,3,7,8,6,5,4
%N A195385 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,sqrt(5),3 right triangle ABC.
%C A195385 See A195284 for definitions and a general discussion.
%e A195385 Philo(ABC,I)=0.6115583512796641306567793224288443270777...
%t A195385 a = 2; b = Sqrt[5]; c = 3; f = 2 a*b/(a + b + c);
%t A195385 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195385 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195385 x3 = f*Sqrt[2]
%t A195385 N[x1, 100]
%t A195385 RealDigits[%]   (* (A) A195381 *)
%t A195385 N[x2, 100]
%t A195385 RealDigits[%]   (* (B) A195383 *)
%t A195385 N[x3, 100]
%t A195385 RealDigits[%]   (* (C) A195384 *)
%t A195385 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195385 RealDigits[%]   (* Philo(ABC,I) A195385 *)
%Y A195385 Cf. A195284.
%K A195385 nonn,cons
%O A195385 0,1
%A A195385 _Clark Kimberling_, Sep 17 2011
%E A195385 a(99) corrected by _Georg Fischer_, Jul 18 2021