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A195406 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of the right triangle ABC having sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

%I A195406 #10 Jul 18 2021 09:59:08
%S A195406 6,0,2,5,6,1,3,9,1,2,8,6,1,1,4,8,6,1,7,9,4,1,5,7,2,2,9,1,1,6,8,4,7,1,
%T A195406 7,8,6,3,8,5,7,4,5,3,6,2,9,6,6,4,0,6,1,3,7,0,4,5,5,2,3,8,4,6,2,3,4,6,
%U A195406 6,8,3,6,1,2,1,4,7,7,2,7,4,9,7,8,2,7,2,9,9,9,0,1,8,7,3,1,3,3,7,5,6
%N A195406 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of  the right triangle ABC having sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).
%C A195406 See A195284 for definitions and a general discussion.
%e A195406 Philo(ABC,I)=0.6025613912861148617941572291168471786...
%t A195406 a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;
%t A195406 f = 2 a*b/(a + b + c);
%t A195406 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195406 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195406 x3 = f*Sqrt[2]
%t A195406 N[x1, 100]
%t A195406 RealDigits[%]    (* (A) A195403 *)
%t A195406 N[x2, 100]
%t A195406 RealDigits[%]    (* (B) A195404 *)
%t A195406 N[x3, 100]
%t A195406 RealDigits[%]    (* (C) A195405 *)
%t A195406 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195406 RealDigits[%]    (*  Philo(ABC,I) A195406 *)
%Y A195406 Cf. A195284.
%K A195406 nonn,cons
%O A195406 0,1
%A A195406 _Clark Kimberling_, Sep 17 2011
%E A195406 a(99) corrected by _Georg Fischer_, Jul 18 2021