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A195358 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,3,sqrt(13) right triangle ABC.

%I A195358 #7 Jul 18 2021 05:37:43
%S A195358 5,8,2,2,5,2,4,7,5,0,6,1,6,5,6,9,9,2,6,4,7,3,2,2,5,5,2,4,7,7,4,9,0,5,
%T A195358 1,0,4,8,9,8,0,6,4,4,4,1,1,5,6,7,0,1,2,1,2,4,4,8,2,9,2,1,7,2,0,3,2,9,
%U A195358 1,2,3,8,5,6,7,8,0,4,2,1,2,2,1,4,0,2,4,9,7,8,8,3,7,7,0,7,4,6,6,0,8
%N A195358 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,3,sqrt(13) right triangle ABC.
%C A195358 See A195284 for definitions and a general discussion.
%e A195358 Philo(ABC,I)=0.582252475061656992647322552477490510489806444115...
%t A195358 a = 2; b = 3; c = Sqrt[13]; f = 2 a*b/(a + b + c);
%t A195358 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195358 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195358 x3 = f*Sqrt[2]
%t A195358 N[x1, 100]
%t A195358 RealDigits[%](* (A) A195355 *)
%t A195358 N[x2, 100]
%t A195358 RealDigits[%](* (B) A195356 *)
%t A195358 N[x3, 100]
%t A195358 RealDigits[%](* (C) A195357 *)
%t A195358 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195358 RealDigits[%](* Philo(ABC,I) A195358 *)
%Y A195358 Cf. A195284.
%K A195358 nonn,cons
%O A195358 0,1
%A A195358 _Clark Kimberling_, Sep 16 2011
%E A195358 a(99) corrected by _Georg Fischer_, Jul 18 2021