A195408 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset: 0

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(B)=0.6119259581259097681148380144011707389...
		

Crossrefs

Cf. A195284.

Programs

Mathematica

a = b - 1; b = (1 + Sqrt[5])/2; c = Sqrt[3];
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) A195407 *)
N[x2, 100]
RealDigits[%]    (* (B) A195408 *)
N[x3, 100]
RealDigits[%]    (* (C) A195409 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195410 *)