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A195340
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)=(1,2,sqrt(5)).
5
7, 8, 4, 9, 2, 9, 6, 8, 4, 7, 6, 4, 4, 3, 4, 9, 4, 5, 2, 0, 1, 7, 2, 4, 3, 6, 3, 4, 5, 6, 7, 3, 5, 6, 7, 2, 6, 9, 4, 4, 4, 6, 1, 4, 2, 6, 3, 0, 2, 4, 6, 6, 8, 1, 0, 5, 5, 5, 4, 4, 8, 5, 5, 7, 9, 2, 3, 8, 2, 7, 5, 4, 4, 9, 4, 8, 3, 1, 3, 4, 8, 5, 5, 6, 0, 9, 0, 1, 9, 1, 7, 7, 8, 0, 0, 9, 1, 1, 6
OFFSET
0,1
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
(A)=0.7849296847644349452017243634567...
MATHEMATICA
a = 1; b = 2; c = Sqrt[5]; 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) A195340 *)
N[x2, 100]
RealDigits[%] (* (B) A195341 *)
N[x3, 100]
RealDigits[%] (* (C) A195342 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195343 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 16 2011
STATUS
approved