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A195366 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)=(sqrt(2),sqrt(3),sqrt(5)).

%I A195366 #8 Dec 24 2017 09:27:20
%S A195366 1,0,0,7,4,6,3,7,4,8,0,3,0,0,5,1,5,9,4,2,9,2,1,1,8,8,4,0,2,6,7,0,6,6,
%T A195366 1,8,1,5,8,0,2,2,0,5,4,3,3,8,2,5,6,7,3,4,0,1,3,7,1,2,8,8,4,0,9,4,8,0,
%U A195366 1,7,9,2,9,6,1,7,9,3,4,2,6,5,0,5,1,2,8,2,9,8,5,7,3,6,4,7,6,6,6,8
%N A195366 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)=(sqrt(2),sqrt(3),sqrt(5)).
%C A195366 See A195284 for definitions and a general discussion.
%H A195366 G. C. Greubel, <a href="/A195366/b195366.txt">Table of n, a(n) for n = 1..10000</a>
%e A195366 (B)=1.007463748030051594292118840267066181580...
%t A195366 a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
%t A195366 f = 2 a*b/(a + b + c);
%t A195366 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195366 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195366 x3 = f*Sqrt[2]
%t A195366 N[x1, 100]
%t A195366 RealDigits[%]    (* (A) A195365 *)
%t A195366 N[x2, 100]
%t A195366 RealDigits[%]    (* (B) A195366 *)
%t A195366 N[x3, 100]
%t A195366 RealDigits[%]    (* (C) A195367 *)
%t A195366 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195366 RealDigits[%]    (* Philo(ABC,I) A195368 *)
%Y A195366 Cf. A195284.
%K A195366 nonn,cons
%O A195366 1,4
%A A195366 _Clark Kimberling_, Sep 16 2011