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A195355
Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(2,3,sqrt(13)).
5
1, 4, 5, 6, 9, 6, 4, 1, 0, 1, 6, 1, 4, 4, 8, 5, 9, 8, 3, 8, 5, 1, 0, 9, 1, 5, 8, 7, 1, 3, 9, 2, 6, 6, 9, 8, 4, 0, 8, 2, 2, 8, 5, 1, 6, 8, 1, 0, 7, 3, 1, 9, 3, 6, 3, 0, 0, 6, 4, 7, 6, 5, 1, 5, 1, 9, 0, 4, 9, 9, 9, 7, 4, 5, 4, 4, 3, 1, 3, 1, 3, 0, 1, 6, 3, 5, 6, 0, 8, 8, 9, 8, 2, 8, 3, 4, 4, 3, 3, 5
OFFSET
1,2
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
(A)=1.45696410161448598385109158713926698408228516810...
MATHEMATICA
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]
RealDigits[%](* (A) A195355 *)
N[x2, 100]
RealDigits[%](* (B) A195356 *)
N[x3, 100]
RealDigits[%](* (C) A195357 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%](* Philo(ABC, I) A195358 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 16 2011
STATUS
approved