A195367 - OEIS

%I #9 Dec 24 2017 09:24:15

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

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

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

%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)=(sqrt(2),sqrt(3),sqrt(5)).

%C See A195284 for definitions and a general discussion.

%H G. C. Greubel, <a href="/A195367/b195367.txt">Table of n, a(n) for n = 1..10000</a>

%e (C)=1.2872120826147987661983905302731728582463923413314...

%t a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];

%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) A195365 *)

%t N[x2, 100]

%t RealDigits[%]    (* (B) A195366 *)

%t N[x3, 100]

%t RealDigits[%]    (* (C) A195367 *)

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

%t RealDigits[%]    (* Philo(ABC,I) A195368 *)

%Y Cf. A195284.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 16 2011