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A195405
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)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).
5
9, 2, 4, 8, 7, 5, 3, 9, 1, 0, 5, 0, 2, 2, 5, 1, 3, 0, 6, 6, 2, 6, 2, 5, 1, 7, 3, 5, 1, 2, 7, 4, 5, 4, 1, 0, 7, 5, 2, 6, 0, 3, 3, 5, 1, 6, 5, 1, 0, 7, 9, 4, 9, 3, 7, 5, 4, 9, 9, 2, 8, 7, 4, 8, 9, 5, 6, 7, 6, 4, 5, 9, 7, 1, 1, 9, 6, 7, 4, 8, 8, 3, 6, 5, 6, 5, 2, 1, 1, 4, 4, 1, 6, 1, 0, 2, 5, 4, 6, 0
OFFSET
0,1
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
(C)=0.92487539105022513066262517351274541075260...
MATHEMATICA
a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/2;
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) A195403 *)
N[x2, 100]
RealDigits[%] (* (B) A195404 *)
N[x3, 100]
RealDigits[%] (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195406 *)
CROSSREFS
Cf. A195284.
Sequence in context: A020784 A111188 A334845 * A089065 A248319 A154398
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
STATUS
approved