A195405 - OEIS

%I #8 May 13 2017 14:18:14

%S 9,2,4,8,7,5,3,9,1,0,5,0,2,2,5,1,3,0,6,6,2,6,2,5,1,7,3,5,1,2,7,4,5,4,

%T 1,0,7,5,2,6,0,3,3,5,1,6,5,1,0,7,9,4,9,3,7,5,4,9,9,2,8,7,4,8,9,5,6,7,

%U 6,4,5,9,7,1,1,9,6,7,4,8,8,3,6,5,6,5,2,1,1,4,4,1,6,1,0,2,5,4,6,0

%N Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

%C See A195284 for definitions and a general discussion.

%e (C)=0.92487539105022513066262517351274541075260...

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

%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) A195403 *)

%t N[x2, 100]

%t RealDigits[%]    (* (B) A195404 *)

%t N[x3, 100]

%t RealDigits[%]    (* (C) A195405 *)

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

%t RealDigits[%]    (*  Philo(ABC,I) A195406 *)

%Y Cf. A195284.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 17 2011