cp's OEIS Frontend

A195370 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)=(1,sqrt(2),sqrt(3)).

%I A195370 #11 Dec 24 2017 09:25:32
%S A195370 7,6,8,1,3,7,4,3,2,6,1,5,5,3,6,7,6,0,7,0,1,5,3,4,5,2,1,1,1,9,2,8,7,9,
%T A195370 5,5,0,9,2,6,7,1,9,8,8,4,5,0,7,8,6,7,6,3,0,3,4,0,7,8,5,3,7,8,0,6,5,4,
%U A195370 5,6,6,3,0,0,7,0,5,7,3,9,6,9,0,4,7,0,2,3,1,0,7,9,2,1,7,7,0,7,3,4
%N A195370 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)=(1,sqrt(2),sqrt(3)).
%C A195370 See A195284 for definitions and a general discussion.
%H A195370 G. C. Greubel, <a href="/A195370/b195370.txt">Table of n, a(n) for n = 0..10000</a>
%e A195370 (B)=0.76813743261553676070153452111928795509267198845...
%t A195370 a = 1; b = Sqrt[2]; c = Sqrt[3];
%t A195370 f = 2 a*b/(a + b + c);
%t A195370 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195370 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195370 x3 = f*Sqrt[2]
%t A195370 N[x1, 100]
%t A195370 RealDigits[%]    (* (A) A195369 *)
%t A195370 N[x2, 100]
%t A195370 RealDigits[%]    (* (B) A195370 *)
%t A195370 N[x3, 100]
%t A195370 RealDigits[%]    (* (C) A195371 *)
%t A195370 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195370 RealDigits[%]    (* Philo(ABC,I) A195372 *)
%Y A195370 Cf. A195284, A195369, A195371, A195372.
%K A195370 nonn,cons
%O A195370 0,1
%A A195370 _Clark Kimberling_, Sep 17 2011