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Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(2,3,sqrt(13)).
5

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

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

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

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

%N Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(2,3,sqrt(13)).

%C See A195284 for definitions and a general discussion.

%e (B)=1.58159112952173055317829635513556895244018458718979885544...

%t a = 2; b = 3; c = Sqrt[13]; 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) A195355 *)

%t N[x2, 100]

%t RealDigits[%](* (B) A195356 *)

%t N[x3, 100]

%t RealDigits[%](* (C) A195357 *)

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

%t RealDigits[%](* Philo(ABC,I) A195358 *)

%Y Cf. A195284.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 16 2011