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A195358
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Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,3,sqrt(13) right triangle ABC.
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5
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5, 8, 2, 2, 5, 2, 4, 7, 5, 0, 6, 1, 6, 5, 6, 9, 9, 2, 6, 4, 7, 3, 2, 2, 5, 5, 2, 4, 7, 7, 4, 9, 0, 5, 1, 0, 4, 8, 9, 8, 0, 6, 4, 4, 4, 1, 1, 5, 6, 7, 0, 1, 2, 1, 2, 4, 4, 8, 2, 9, 2, 1, 7, 2, 0, 3, 2, 9, 1, 2, 3, 8, 5, 6, 7, 8, 0, 4, 2, 1, 2, 2, 1, 4, 0, 2, 4, 9, 7, 8, 8, 3, 7, 7, 0, 7, 4, 6, 6, 0, 8
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OFFSET
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0,1
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COMMENTS
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See A195284 for definitions and a general discussion.
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LINKS
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EXAMPLE
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Philo(ABC,I)=0.582252475061656992647322552477490510489806444115...
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MATHEMATICA
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a = 2; b = 3; c = Sqrt[13]; 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]
N[x2, 100]
N[x3, 100]
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%](* Philo(ABC, I) A195358 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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