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A195389
Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(5),sqrt(7) right triangle ABC.
5
5, 7, 3, 8, 9, 4, 9, 4, 2, 7, 4, 8, 6, 8, 2, 3, 0, 6, 8, 5, 9, 4, 1, 0, 2, 1, 1, 4, 2, 6, 4, 4, 0, 2, 2, 8, 6, 9, 3, 9, 8, 0, 8, 1, 9, 5, 3, 5, 4, 9, 9, 1, 1, 5, 0, 5, 7, 5, 2, 0, 9, 5, 2, 0, 9, 2, 4, 5, 4, 7, 0, 8, 0, 9, 5, 1, 8, 9, 1, 7, 5, 0, 5, 0, 8, 1, 2, 7, 6, 3, 1, 2, 8, 9, 1, 0, 5, 0, 7, 7
OFFSET
0,1
COMMENTS
See A195284 for definitions and a general discussion.
LINKS
EXAMPLE
Philo(ABC,I)=0.5738949427486823068594102114264402286939808...
MATHEMATICA
a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];
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) A195386 *)
N[x2, 100]
RealDigits[%] (* (A) A195387 *)
N[x3, 100]
RealDigits[%] (* (A) A195388 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195389 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
STATUS
approved