A195371 - OEIS

%I #10 Dec 24 2017 09:25:37

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

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

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

%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(2),sqrt(3)).

%C See A195284 for definitions and a general discussion.

%H G. C. Greubel, <a href="/A195371/b195371.txt">Table of n, a(n) for n = 0..10000</a>

%e (C)=0.96472381958991695060440464950380668660...

%t a = 1; b = Sqrt[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) A195369 *)

%t N[x2, 100]

%t RealDigits[%]    (* (B) A195370 *)

%t N[x3, 100]

%t RealDigits[%]    (* (C) A195371 *)

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

%t RealDigits[%]    (* Philo(ABC,I) A195372 *)

%Y Cf. A195284, A195369, A195370, A195372.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 17 2011