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A195383
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)=(2,sqrt(5),3).
5
1, 3, 5, 4, 0, 4, 4, 6, 2, 7, 7, 7, 2, 8, 4, 5, 8, 7, 1, 2, 8, 3, 3, 4, 4, 5, 0, 9, 1, 0, 4, 2, 8, 7, 1, 2, 4, 0, 6, 0, 4, 5, 8, 0, 9, 0, 6, 6, 0, 7, 0, 3, 6, 1, 9, 9, 7, 8, 9, 0, 3, 6, 6, 7, 7, 8, 5, 9, 7, 3, 8, 2, 3, 2, 1, 1, 8, 6, 9, 5, 5, 8, 9, 3, 8, 1, 4, 2, 5, 6, 0, 7, 7, 6, 8, 9, 8, 9, 8, 3
OFFSET
1,2
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
(B)=1.354044627772845871283344509104287124060458090...
MATHEMATICA
a = 2; b = Sqrt[5]; c = 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) A195381 *)
N[x2, 100]
RealDigits[%] (* (B) A195383 *)
N[x3, 100]
RealDigits[%] (* (C) A195384 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195385 *)
CROSSREFS
Cf. A195284.
Sequence in context: A366857 A065974 A096822 * A303069 A086567 A016611
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
STATUS
approved