cp's OEIS Frontend

A195408 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)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).

%I A195408 #8 May 13 2017 14:24:42
%S A195408 6,1,1,9,2,5,9,5,8,1,2,5,9,0,9,7,6,8,1,1,4,8,3,8,0,1,4,4,0,1,1,7,0,7,
%T A195408 3,8,9,1,9,7,3,5,9,3,3,2,2,6,3,5,9,0,0,3,8,0,1,2,5,7,4,9,5,7,9,0,0,8,
%U A195408 0,7,8,3,8,6,7,6,4,6,9,8,7,4,1,9,9,1,3,8,6,4,4,5,1,1,6,1,9,8,2,0
%N A195408 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)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).
%C A195408 See A195284 for definitions and a general discussion.
%e A195408 (B)=0.6119259581259097681148380144011707389...
%t A195408 a = b - 1; b = (1 + Sqrt[5])/2; c = Sqrt[3];
%t A195408 f = 2 a*b/(a + b + c);
%t A195408 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195408 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195408 x3 = f*Sqrt[2]
%t A195408 N[x1, 100]
%t A195408 RealDigits[%]    (* (A) A195407 *)
%t A195408 N[x2, 100]
%t A195408 RealDigits[%]    (* (B) A195408 *)
%t A195408 N[x3, 100]
%t A195408 RealDigits[%]    (* (C) A195409 *)
%t A195408 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195408 RealDigits[%]    (*  Philo(ABC,I) A195410 *)
%Y A195408 Cf. A195284.
%K A195408 nonn,cons
%O A195408 0,1
%A A195408 _Clark Kimberling_, Sep 17 2011