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A195343 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,2,sqrt(5) right triangle ABC.

%I A195343 #7 Jul 18 2021 05:31:34
%S A195343 5,2,7,7,5,2,6,3,3,6,0,7,7,1,0,3,5,6,1,1,8,2,1,4,2,9,0,2,9,3,9,4,9,5,
%T A195343 2,2,3,8,0,4,0,2,1,3,5,2,9,2,0,4,0,2,9,8,3,5,1,1,8,0,3,5,8,9,3,0,7,0,
%U A195343 2,0,3,8,2,2,5,3,2,5,8,9,8,0,5,2,1,1,3,4,1,4,7,7,9,8,1,3,4,3,6,5,7
%N A195343 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,2,sqrt(5) right triangle ABC.
%C A195343 See A195284 for definitions and a general discussion.
%e A195343 Philo(ABC,I)=0.5277526336077103561182142902939495223804021352...
%t A195343 a = 1; b = 2; c = Sqrt[5]; f = 2*a*b/(a + b + c);
%t A195343 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ];
%t A195343 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ];
%t A195343 x3 = f*Sqrt[2];
%t A195343 N[x1, 100]
%t A195343 RealDigits[%] (* (A) A195340 *)
%t A195343 N[x2, 100]
%t A195343 RealDigits[%] (* (B) A195341 *)
%t A195343 N[x3, 100]
%t A195343 RealDigits[%] (* (C) A195342 *)
%t A195343 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195343 RealDigits[%] (* Philo(ABC,I) A195343 *)
%Y A195343 Cf. A195284.
%K A195343 nonn,cons
%O A195343 0,1
%A A195343 _Clark Kimberling_, Sep 16 2011
%E A195343 a(99) corrected by _Georg Fischer_, Jul 18 2021