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A195343
Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,2,sqrt(5) right triangle ABC.
5
5, 2, 7, 7, 5, 2, 6, 3, 3, 6, 0, 7, 7, 1, 0, 3, 5, 6, 1, 1, 8, 2, 1, 4, 2, 9, 0, 2, 9, 3, 9, 4, 9, 5, 2, 2, 3, 8, 0, 4, 0, 2, 1, 3, 5, 2, 9, 2, 0, 4, 0, 2, 9, 8, 3, 5, 1, 1, 8, 0, 3, 5, 8, 9, 3, 0, 7, 0, 2, 0, 3, 8, 2, 2, 5, 3, 2, 5, 8, 9, 8, 0, 5, 2, 1, 1, 3, 4, 1, 4, 7, 7, 9, 8, 1, 3, 4, 3, 6, 5, 7
OFFSET
0,1
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
Philo(ABC,I)=0.5277526336077103561182142902939495223804021352...
MATHEMATICA
a = 1; b = 2; c = Sqrt[5]; 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) A195340 *)
N[x2, 100]
RealDigits[%] (* (B) A195341 *)
N[x3, 100]
RealDigits[%] (* (C) A195342 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195343 *)
CROSSREFS
Cf. A195284.
Sequence in context: A354827 A364521 A253545 * A074454 A256110 A267211
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 16 2011
EXTENSIONS
a(99) corrected by Georg Fischer, Jul 18 2021
STATUS
approved