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

%I #5 Mar 30 2012 18:57:45

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

%C See A195284 for definitions and a general discussion.

%e Philo(ABC,I)=0.4746287747584270516471193113995166804876...

%t a = 2; b = 5; c = Sqrt[29]; f = 2 a*b/(a + b + c);

%t x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]

%t x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]

%t x3 = f*Sqrt[2]

%t N[x1, 100]

%t RealDigits[%] (* (A) A195359 *)

%t N[x2, 100]

%t RealDigits[%] (* (B) A195360 *)

%t N[x3, 100]

%t RealDigits[%] (* (C) A195361 *)

%t N[(x1 + x2 + x3)/(a + b + c), 100]

%t RealDigits[%] (* Philo(ABC,I) A195362 *)

%Y Cf. A195284.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 16 2011