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A195402 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(7),3,4 right triangle ABC.

%I A195402 #8 May 13 2017 14:47:56
%S A195402 6,1,0,8,8,9,7,8,0,3,8,6,3,8,0,0,0,7,4,4,2,4,1,2,8,8,8,6,7,4,0,4,2,2,
%T A195402 3,3,0,2,5,7,0,5,2,7,6,9,0,4,5,9,2,0,9,4,1,1,5,0,6,5,9,3,5,1,6,6,1,7,
%U A195402 2,9,2,4,7,9,6,2,1,7,7,0,5,9,3,1,4,8,2,1,9,7,9,6,3,6,3,8,7,7,3,2
%N A195402 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(7),3,4 right triangle ABC.
%C A195402 See A195284 for definitions and a general discussion.
%e A195402 Philo(ABC,I)=0.6108897803863800074424128886740422330...
%t A195402 a = Sqrt[7]; b = 3; c = 4;
%t A195402 f = 2 a*b/(a + b + c);
%t A195402 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195402 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195402 x3 = f*Sqrt[2]
%t A195402 N[x1, 100]
%t A195402 RealDigits[%]    (* (A) A195399 *)
%t A195402 N[x2, 100]
%t A195402 RealDigits[%]    (* (B) A195400 *)
%t A195402 N[x3, 100]
%t A195402 RealDigits[%]    (* (C) A195401 *)
%t A195402 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195402 RealDigits[%]    (*  Philo(ABC,I) A195402 *)
%Y A195402 Cf. A195284.
%K A195402 nonn,cons
%O A195402 0,1
%A A195402 _Clark Kimberling_, Sep 17 2011