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 A195299 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(28,45,53). 4
 2, 2, 8, 7, 9, 1, 7, 8, 0, 9, 1, 0, 8, 2, 2, 2, 2, 9, 2, 3, 9, 9, 4, 1, 5, 4, 3, 6, 4, 8, 8, 3, 4, 4, 4, 3, 9, 7, 1, 0, 8, 4, 4, 7, 6, 0, 7, 7, 5, 9, 9, 0, 4, 2, 7, 1, 6, 5, 4, 6, 8, 0, 0, 9, 1, 9, 9, 5, 6, 9, 3, 6, 1, 7, 7, 7, 2, 8, 6, 3, 9, 4, 2, 2, 8, 7, 8, 9, 5, 5, 8, 5, 2, 3, 9, 0, 3, 4, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS See A195284 for definitions and a general discussion. LINKS EXAMPLE (C)= MATHEMATICA a = 28; b = 45; c = 53; h = a (a + c)/(a + b + c); k = a*b/(a + b + c); 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) A195298 *) 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] (* (B) A195299 *) 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] (* (C)=20*sqrt(2) *) (f1 + f2 + f3)/(a + b + c) RealDigits[%, 10, 100]  (* Phil(ABC, I), A195300 *) CROSSREFS Cf. A195284. Sequence in context: A197820 A064862 A123202 * A095297 A195138 A094887 Adjacent sequences:  A195296 A195297 A195298 * A195300 A195301 A195302 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 14 2011 STATUS approved

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