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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).
5
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
0,1
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
Philo(ABC,I)=0.4629992818729451452524915088005478716250...
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 *)
CROSSREFS
Cf. A195284.
Sequence in context: A171547 A114579 A021220 * A095196 A074828 A282028
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
EXTENSIONS
a(99) corrected by Georg Fischer, Jul 18 2021
STATUS
approved