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A195356 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)).

%I A195356 #5 Mar 30 2012 18:57:45
%S A195356 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 A195356 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 A195356 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 A195356 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 A195356 See A195284 for definitions and a general discussion.
%e A195356 (B)=1.58159112952173055317829635513556895244018458718979885544...
%t A195356 a = 2; b = 3; c = Sqrt[13]; f = 2 a*b/(a + b + c);
%t A195356 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195356 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195356 x3 = f*Sqrt[2]
%t A195356 N[x1, 100]
%t A195356 RealDigits[%](* (A) A195355 *)
%t A195356 N[x2, 100]
%t A195356 RealDigits[%](* (B) A195356 *)
%t A195356 N[x3, 100]
%t A195356 RealDigits[%](* (C) A195357 *)
%t A195356 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195356 RealDigits[%](* Philo(ABC,I) A195358 *)
%Y A195356 Cf. A195284.
%K A195356 nonn,cons
%O A195356 1,2
%A A195356 _Clark Kimberling_, Sep 16 2011