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A195369 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(2),sqrt(3)).

%I A195369 #9 Dec 24 2017 09:27:23
%S A195369 7,1,5,7,9,0,1,3,5,9,8,9,9,1,4,9,5,4,5,9,5,4,9,2,6,7,2,3,3,3,4,3,2,4,
%T A195369 9,4,5,6,6,3,6,8,3,0,6,5,6,7,0,5,1,1,4,4,1,8,8,8,6,9,2,2,0,1,8,3,4,5,
%U A195369 3,8,4,6,2,9,2,9,5,3,1,9,3,5,2,3,4,0,5,2,5,0,1,4,2,2,0,5,7,7,6,9
%N A195369 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(2),sqrt(3)).
%C A195369 See A195284 for definitions and a general discussion.
%H A195369 G. C. Greubel, <a href="/A195369/b195369.txt">Table of n, a(n) for n = 0..10000</a>
%e A195369 (A)=0.7157901359899149545954926723334324945663...
%t A195369 a = 1; b = Sqrt[2]; c = Sqrt[3];
%t A195369 f = 2 a*b/(a + b + c);
%t A195369 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195369 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195369 x3 = f*Sqrt[2]
%t A195369 N[x1, 100]
%t A195369 RealDigits[%]    (* (A) A195369 *)
%t A195369 N[x2, 100]
%t A195369 RealDigits[%]    (* (B) A195370 *)
%t A195369 N[x3, 100]
%t A195369 RealDigits[%]    (* (C) A195371 *)
%t A195369 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195369 RealDigits[%]    (* Philo(ABC,I) A195372 *)
%Y A195369 Cf. A195284, A195370, A195371, A195372.
%K A195369 nonn,cons
%O A195369 0,1
%A A195369 _Clark Kimberling_, Sep 17 2011