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A195395 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(3),sqrt(5),sqrt(8)).

%I A195395 #6 Mar 30 2012 18:57:45
%S A195395 1,2,0,4,4,9,9,9,5,2,4,3,8,3,0,0,4,2,2,9,6,2,6,7,7,2,0,4,9,5,5,8,8,0,
%T A195395 4,2,5,3,7,2,4,9,9,8,3,8,1,4,3,2,7,9,8,3,2,8,9,2,3,7,3,3,6,2,4,6,2,0,
%U A195395 5,8,0,7,9,0,1,7,0,6,1,9,5,8,9,3,3,1,3,9,8,9,3,0,0,9,4,1,9,1,5,1
%N A195395 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(3),sqrt(5),sqrt(8)).
%C A195395 See A195284 for definitions and a general discussion.
%e A195395 (A)=1.204499952438300422962677204955880425372499...
%t A195395 a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
%t A195395 f = 2 a*b/(a + b + c);
%t A195395 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195395 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195395 x3 = f*Sqrt[2]
%t A195395 N[x1, 100]
%t A195395 RealDigits[%]    (* (A) A195395 *)
%t A195395 N[x2, 100]
%t A195395 RealDigits[%]    (* (B) A195396 *)
%t A195395 N[x3, 100]
%t A195395 RealDigits[%]    (* (C) A195397 *)
%t A195395 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195395 RealDigits[%]    (*  Philo(ABC,I) A195398 *)
%Y A195395 Cf. A195284, A195896, A195897, A195398.
%K A195395 nonn,cons
%O A195395 1,2
%A A195395 _Clark Kimberling_, Sep 17 2011