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A195398 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(3),sqrt(5),sqrt(8) right triangle ABC.

%I A195398 #7 Jul 18 2021 05:44:43
%S A195398 6,0,1,1,2,6,3,9,6,9,1,7,6,5,3,2,5,1,6,5,4,1,2,6,3,7,8,7,7,7,2,6,1,0,
%T A195398 8,0,6,6,8,6,4,0,3,9,9,9,2,3,8,7,2,4,8,9,7,2,4,2,0,2,9,3,6,6,1,0,0,0,
%U A195398 5,1,7,6,6,5,0,8,6,4,9,9,1,2,4,1,5,6,1,6,4,8,7,5,9,2,4,6,1,9,2,3,6,8,9
%N A195398 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(3),sqrt(5),sqrt(8) right triangle ABC.
%C A195398 See A195284 for definitions and a general discussion.
%e A195398 Philo(ABC,I)=0.6011263969176532516541263787772610806686403999...
%t A195398 a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
%t A195398 f = 2 a*b/(a + b + c);
%t A195398 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195398 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195398 x3 = f*Sqrt[2]
%t A195398 N[x1, 100]
%t A195398 RealDigits[%]    (* (A) A195395 *)
%t A195398 N[x2, 100]
%t A195398 RealDigits[%]    (* (B) A195396 *)
%t A195398 N[x3, 100]
%t A195398 RealDigits[%]    (* (C) A195397 *)
%t A195398 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195398 RealDigits[%]    (*  Philo(ABC,I) A195398 *)
%Y A195398 Cf. A195284.
%K A195398 nonn,cons
%O A195398 0,1
%A A195398 _Clark Kimberling_, Sep 17 2011
%E A195398 a(99) corrected by _Georg Fischer_, Jul 18 2021