A195408 - OEIS

%I #8 May 13 2017 14:24:42

%S 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 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 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 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 See A195284 for definitions and a general discussion.

%e (B)=0.6119259581259097681148380144011707389...

%t a = b - 1; b = (1 + Sqrt[5])/2; c = Sqrt[3];

%t f = 2 a*b/(a + b + c);

%t x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]

%t x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]

%t x3 = f*Sqrt[2]

%t N[x1, 100]

%t RealDigits[%]    (* (A) A195407 *)

%t N[x2, 100]

%t RealDigits[%]    (* (B) A195408 *)

%t N[x3, 100]

%t RealDigits[%]    (* (C) A195409 *)

%t N[(x1 + x2 + x3)/(a + b + c), 100]

%t RealDigits[%]    (*  Philo(ABC,I) A195410 *)

%Y Cf. A195284.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 17 2011