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 A195475 Decimal expansion of shortest length, (A), of segment from side AB through centroid to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(3),2) and angles 30,60,90. 1
 6, 4, 3, 8, 4, 6, 3, 1, 3, 2, 9, 8, 7, 4, 3, 5, 3, 1, 5, 6, 9, 3, 7, 2, 1, 0, 7, 2, 1, 1, 8, 0, 9, 7, 2, 0, 6, 7, 5, 1, 9, 8, 1, 6, 0, 8, 2, 1, 8, 5, 8, 7, 2, 8, 7, 9, 9, 8, 8, 4, 7, 9, 2, 4, 7, 7, 6, 0, 4, 9, 3, 3, 7, 6, 7, 7, 9, 9, 8, 3, 9, 1, 9, 0, 0, 8, 7, 9, 2, 8, 3, 1, 3, 7, 8, 0, 4, 6, 5, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A195304 for definitions and a general discussion. LINKS EXAMPLE (A)=0.643846313298743531569372107211809720... MATHEMATICA a = 1; b = Sqrt[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) A195575 *) 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) A195576 *) 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, 4] RealDigits[%, 10, 100] (* (C) A195577 *) c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c) RealDigits[%, 10, 100] (* Philo(ABC, G) A195578 *) CROSSREFS Cf. A195304, A195476, A195477, A195478. Sequence in context: A079624 A035335 A011097 * A321786 A188725 A306591 Adjacent sequences:  A195472 A195473 A195474 * A195476 A195477 A195478 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 19 2011 STATUS approved

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Last modified May 25 17:53 EDT 2020. Contains 334595 sequences. (Running on oeis4.)