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A195482
Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the 2,sqrt(5),3 right triangle ABC.
5
6, 3, 5, 2, 6, 8, 6, 0, 4, 8, 3, 9, 3, 3, 6, 2, 1, 8, 8, 1, 1, 5, 0, 6, 2, 7, 8, 2, 7, 6, 4, 4, 5, 8, 5, 2, 0, 1, 9, 8, 1, 8, 7, 6, 3, 7, 9, 6, 2, 3, 1, 6, 4, 1, 6, 6, 5, 4, 9, 0, 3, 9, 5, 0, 9, 2, 3, 2, 4, 9, 7, 4, 7, 8, 4, 8, 9, 0, 1, 9, 2, 5, 2, 7, 0, 1, 9, 9, 5, 0, 1, 6, 9, 5, 6, 6, 2, 1, 2, 8
OFFSET
0,1
See A195304 for definitions and a general discussion.
EXAMPLE
Philo(ABC,G)=0.635268604839336218811506278276445852019818763...
MATHEMATICA
a = 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) A195479 *)
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) A195480 *)
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) A195481 *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC, G) A195482 *)
CROSSREFS
Cf. A195304.
Sequence in context: A228725 A286982 A153595 * A298529 A245273 A199728
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 19 2011
STATUS
approved

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Last modified September 20 04:19 EDT 2024. Contains 376016 sequences. (Running on oeis4.)