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A195397
Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).
5
1, 6, 1, 1, 7, 6, 7, 4, 0, 2, 9, 5, 1, 5, 5, 7, 4, 3, 0, 1, 9, 6, 1, 7, 7, 6, 1, 9, 1, 3, 8, 6, 0, 9, 9, 2, 5, 6, 8, 5, 5, 0, 2, 6, 1, 9, 9, 8, 1, 8, 8, 6, 9, 5, 5, 2, 9, 0, 1, 9, 7, 4, 2, 0, 0, 4, 3, 5, 5, 4, 8, 1, 6, 0, 9, 6, 5, 5, 3, 2, 4, 7, 8, 8, 4, 1, 0, 7, 5, 4, 1, 4, 8, 3, 9, 4, 0, 5, 3, 0
OFFSET
1,2
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
(C)=1.6117674029515574301961776191386099256...
MATHEMATICA
a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
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) A195395 *)
N[x2, 100]
RealDigits[%] (* (B) A195396 *)
N[x3, 100]
RealDigits[%] (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195398 *)
CROSSREFS
Cf. A195284.
Sequence in context: A138072 A176348 A176264 * A173741 A171147 A171695
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
STATUS
approved