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A195362 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,5,sqrt(29) right triangle ABC.

%I A195362 #5 Mar 30 2012 18:57:45
%S A195362 4,7,4,6,2,8,7,7,4,7,5,8,4,2,7,0,5,1,6,4,7,1,1,9,3,1,1,3,9,9,5,1,6,6,
%T A195362 8,0,4,8,7,6,6,6,3,6,8,5,9,7,0,9,3,2,6,8,8,7,1,3,8,9,6,7,5,8,4,3,8,6,
%U A195362 6,8,5,9,6,5,5,7,5,2,0,7,3,2,7,5,7,2,8,8,3,5,4,7,1,9,8,2,9,4,9,5
%N A195362 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,5,sqrt(29) right triangle ABC.
%C A195362 See A195284 for definitions and a general discussion.
%e A195362 Philo(ABC,I)=0.4746287747584270516471193113995166804876...
%t A195362 a = 2; b = 5; c = Sqrt[29]; f = 2 a*b/(a + b + c);
%t A195362 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195362 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195362 x3 = f*Sqrt[2]
%t A195362 N[x1, 100]
%t A195362 RealDigits[%]    (* (A) A195359 *)
%t A195362 N[x2, 100]
%t A195362 RealDigits[%]    (* (B) A195360 *)
%t A195362 N[x3, 100]
%t A195362 RealDigits[%]    (* (C) A195361 *)
%t A195362 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195362 RealDigits[%]    (* Philo(ABC,I)  A195362 *)
%Y A195362 Cf. A195284.
%K A195362 nonn,cons
%O A195362 0,1
%A A195362 _Clark Kimberling_, Sep 16 2011