A195348 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.

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, 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, 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

Offset: 0

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=0.7578747639260239988121867474270095303467925401944...
(A)=(4*sqrt(6-3*sqrt(3)))/(3+sqrt(3))
(B)=2-(2/3)sqrt(3)
(C)=sqrt(6)-sqrt(2)
		

Crossrefs

Cf. A195284, A093821, A120683, A195380.

Programs

Mathematica

a = 1; b = Sqrt[3]; c = 2;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%] (* (A) A195348 *)
N[x2, 100]
RealDigits[%] (* (B) A093821 *)
N[x3, 100]
RealDigits[%] (* (C) A120683 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* A195380 *)