A195410 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of the right triangle ABC having sidelengths (a,b,c)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset: 0

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			Philo(ABC,I)=0.4629992818729451452524915088005478716250...
		

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 *)

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021