A195344 - OEIS

%I #5 Mar 30 2012 18:57:45

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

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

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

%N Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,3,sqrt(10)).

%C See A195284 for definitions and a general discussion.

%e (A)=0.84868096879341596813098974830298515938184618...

%t a = 1; b = 3; c = Sqrt[10]; 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[%]  (* A195344 *)

%t N[x2, 100]

%t RealDigits[%] (* A195345 *)

%t N[x3, 100]

%t RealDigits[%] (* A195346 *)

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

%t RealDigits[%] (* A195347 *)

%Y Cf. A195284, A195345, A195346, A195347.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 16 2011