A195348 - OEIS

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

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

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

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

%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,sqrt(3),2) and vertex angles of degree measure 30,60,90.

%C See A195284 for definitions and a general discussion.

%e (A)=0.7578747639260239988121867474270095303467925401944...

%e (A)=(4*sqrt(6-3*sqrt(3)))/(3+sqrt(3))

%e (B)=2-(2/3)sqrt(3)

%e (C)=sqrt(6)-sqrt(2)

%t a = 1; b = Sqrt[3]; c = 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) A195348 *)

%t N[x2, 100]

%t RealDigits[%] (* (B) A093821 *)

%t N[x3, 100]

%t RealDigits[%] (* (C) A120683 *)

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

%t RealDigits[%] (* A195380 *)

%Y Cf. A195284, A093821, A120683, A195380.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 17 2011