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 A195473 Decimal expansion of shortest length, (C), of segment from side CA through centroid to side CB in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(2),sqrt(3)). 5
 8, 3, 1, 9, 7, 7, 5, 6, 0, 2, 8, 9, 1, 6, 3, 2, 0, 4, 5, 9, 3, 0, 2, 3, 8, 1, 1, 4, 8, 1, 9, 6, 7, 8, 2, 7, 4, 4, 1, 2, 5, 0, 3, 0, 4, 9, 9, 1, 9, 8, 6, 7, 8, 3, 5, 4, 9, 3, 4, 1, 1, 3, 7, 0, 4, 5, 9, 1, 4, 2, 8, 7, 4, 9, 7, 7, 6, 9, 9, 2, 5, 9, 7, 0, 5, 8, 3, 3, 2, 4, 3, 6, 9, 8, 7, 6, 3, 7, 8, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A195304 for definitions and a general discussion. LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 EXAMPLE (C)=0.8319775602891632045930238114819678... MATHEMATICA a = 1; b = Sqrt[2]; 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) A195471 *) 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) A195472 *) 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) A195473 *) c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c) RealDigits[%, 10, 100] (* Philo(ABC, G) A195474 *) CROSSREFS Cf. A195304. Sequence in context: A019782 A221209 A056030 * A195728 A214406 A176454 Adjacent sequences:  A195470 A195471 A195472 * A195474 A195475 A195476 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 19 2011 STATUS approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)