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A195484
Decimal expansion of shortest length, (B), of segment from side BC through centroid to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)).
5
1, 7, 0, 6, 0, 4, 6, 3, 5, 0, 3, 4, 4, 2, 3, 2, 4, 4, 2, 2, 8, 5, 4, 1, 9, 9, 0, 4, 0, 9, 8, 4, 7, 0, 6, 0, 7, 6, 2, 3, 6, 8, 0, 2, 8, 8, 7, 3, 0, 0, 1, 5, 3, 3, 5, 0, 3, 6, 2, 4, 1, 9, 6, 8, 3, 9, 0, 7, 0, 1, 0, 6, 1, 2, 2, 0, 0, 2, 7, 4, 7, 9, 4, 9, 7, 7, 8, 4, 3, 2, 5, 8, 8, 0, 1, 6, 8, 6, 3, 5
OFFSET
1,2
See A195304 for definitions and a general discussion.
EXAMPLE
(B)=1.7060463503442324422854199040984706076236802887300...
MATHEMATICA
a = Sqrt[2]; b = Sqrt[5]; h = 2 a/3; k = b/3;
f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f1 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (A) A195483 *)
f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f2 = (f[t])^(1/2) /. Part[s, 4]
RealDigits[%, 10, 100] (* (B) A195484 *)
f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
s = NSolve[D[f[t], t] == 0, t, 150]
f3 = (f[t])^(1/2) /. Part[s, 1]
RealDigits[%, 10, 100] (* (C) A195485 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC, G) A195486 *)
CROSSREFS
Cf. A195304.
Sequence in context: A193012 A264758 A362149 * A130203 A328717 A011479
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 19 2011
STATUS
approved

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Last modified September 20 17:28 EDT 2024. Contains 376075 sequences. (Running on oeis4.)