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A195365 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)=(sqrt(2),sqrt(3),sqrt(5)).

%I A195365 #9 Dec 24 2017 09:27:17
%S A195365 9,6,6,2,7,3,9,6,1,5,7,6,7,1,2,9,5,7,2,0,9,3,8,8,6,4,9,0,0,9,2,1,2,4,
%T A195365 8,1,6,3,4,4,4,6,9,2,6,1,3,1,5,3,9,1,4,2,4,2,6,3,4,9,7,1,5,7,5,1,3,2,
%U A195365 2,7,8,5,0,7,6,4,4,7,6,0,1,3,2,0,4,7,0,9,0,0,1,3,2,9,1,2,4,2,1,1
%N A195365 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)=(sqrt(2),sqrt(3),sqrt(5)).
%C A195365 See A195284 for definitions and a general discussion.
%H A195365 G. C. Greubel, <a href="/A195365/b195365.txt">Table of n, a(n) for n = 0..10000</a>
%e A195365 (A)=0.96627396157671295720938864900921248163444...
%t A195365 a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
%t A195365 f = 2 a*b/(a + b + c);
%t A195365 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195365 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195365 x3 = f*Sqrt[2]
%t A195365 N[x1, 100]
%t A195365 RealDigits[%]    (* (A) A195365 *)
%t A195365 N[x2, 100]
%t A195365 RealDigits[%]    (* (B) A195366 *)
%t A195365 N[x3, 100]
%t A195365 RealDigits[%]    (* (C) A195367 *)
%t A195365 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195365 RealDigits[%]     (* Philo(ABC,I) A195368 *)
%Y A195365 Cf. A195284, A195366, A195367, A195368.
%K A195365 nonn,cons
%O A195365 0,1
%A A195365 _Clark Kimberling_, Sep 16 2011