A195384 - OEIS

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

%S 1,7,4,8,0,6,4,0,9,7,7,9,5,2,8,4,2,8,3,1,9,7,2,0,4,8,2,0,2,2,3,0,2,0,

%T 4,5,5,1,4,9,8,8,3,2,6,3,9,4,8,2,6,8,7,5,3,6,8,0,8,2,5,1,1,4,8,0,1,8,

%U 6,1,9,6,0,1,7,7,1,3,1,1,8,2,4,9,3,8,6,0,5,7,4,0,5,1,6,5,8,7,2,2

%N Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(2,sqrt(5),3).

%C See A195284 for definitions and a general discussion.

%e (C)=1.74806409779528428319720482022302045514988...

%t a = 2; b = Sqrt[5]; c = 3; 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) A195381 *)

%t N[x2, 100]

%t RealDigits[%]   (* (B) A195383 *)

%t N[x3, 100]

%t RealDigits[%]   (* (C) A195384 *)

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

%t RealDigits[%]   (* Philo(ABC,I) A195385 *)

%Y Cf. A195284.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 17 2011