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 A195490 Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the sqrt(7),3,4 right triangle ABC. 5
 6, 3, 5, 0, 0, 3, 8, 3, 3, 3, 3, 6, 2, 3, 7, 3, 5, 2, 4, 7, 0, 2, 1, 2, 1, 9, 0, 3, 6, 9, 3, 5, 0, 3, 5, 9, 3, 1, 9, 3, 7, 8, 2, 0, 9, 4, 7, 3, 1, 4, 8, 3, 5, 1, 7, 0, 6, 8, 1, 4, 0, 6, 5, 2, 9, 7, 0, 2, 5, 4, 4, 1, 6, 5, 9, 8, 5, 1, 3, 1, 3, 7, 7, 1, 4, 9, 2, 3, 0, 8, 8, 2, 4, 9, 0, 9, 4, 6, 4, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A195304 for definitions and a general discussion. LINKS Table of n, a(n) for n=0..99. EXAMPLE Philo(ABC,G)=0.635003833336237352470212190369350359... MATHEMATICA a = Sqrt[7]; b = 3; 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) A195487 *) 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) A195488 *) 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) A195489 *) c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c) RealDigits[%, 10, 100] (* Philo(ABC, G) A195490 *) CROSSREFS Cf. A195304. Sequence in context: A363688 A019150 A019165 * A195471 A305187 A065418 Adjacent sequences: A195487 A195488 A195489 * A195491 A195492 A195493 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 19 2011 STATUS approved

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)