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A195370
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Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(2),sqrt(3)).
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5
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7, 6, 8, 1, 3, 7, 4, 3, 2, 6, 1, 5, 5, 3, 6, 7, 6, 0, 7, 0, 1, 5, 3, 4, 5, 2, 1, 1, 1, 9, 2, 8, 7, 9, 5, 5, 0, 9, 2, 6, 7, 1, 9, 8, 8, 4, 5, 0, 7, 8, 6, 7, 6, 3, 0, 3, 4, 0, 7, 8, 5, 3, 7, 8, 0, 6, 5, 4, 5, 6, 6, 3, 0, 0, 7, 0, 5, 7, 3, 9, 6, 9, 0, 4, 7, 0, 2, 3, 1, 0, 7, 9, 2, 1, 7, 7, 0, 7, 3, 4
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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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(B)=0.76813743261553676070153452111928795509267198845...
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MATHEMATICA
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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]
N[x2, 100]
N[x3, 100]
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195372 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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