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A195372
Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(2),sqrt(3) right triangle ABC.
5
5, 9, 0, 5, 6, 8, 0, 8, 0, 0, 1, 5, 9, 9, 7, 1, 3, 4, 3, 7, 4, 7, 0, 4, 6, 4, 4, 1, 6, 4, 6, 5, 0, 5, 6, 6, 9, 4, 4, 1, 0, 3, 2, 9, 4, 1, 9, 3, 4, 2, 2, 8, 8, 8, 7, 8, 2, 6, 1, 4, 8, 0, 1, 3, 7, 9, 5, 6, 6, 0, 0, 7, 2, 4, 2, 4, 6, 8, 5, 7, 1, 9, 9, 1, 0, 8, 4, 5, 3, 9, 5, 3, 6, 8, 5, 5, 6, 5, 0, 7
OFFSET
0,1
COMMENTS
See A195284 for definitions and a general discussion.
LINKS
EXAMPLE
Philo(ABC,I)=0.590568080015997134374704644164650566944103294...
MATHEMATICA
a = 1; b = Sqrt[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) A195369 *)
N[x2, 100]
RealDigits[%] (* (B) A195370 *)
N[x3, 100]
RealDigits[%] (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195372 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
STATUS
approved