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 A195290 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(7,24,25). 3
 6, 0, 6, 0, 9, 1, 5, 2, 6, 7, 3, 1, 3, 2, 6, 4, 4, 9, 4, 8, 6, 4, 3, 8, 0, 2, 4, 6, 6, 1, 2, 9, 9, 1, 7, 6, 5, 2, 9, 8, 5, 9, 3, 7, 5, 1, 6, 1, 5, 4, 9, 1, 7, 4, 2, 1, 8, 5, 7, 7, 0, 3, 0, 5, 6, 7, 4, 5, 6, 7, 7, 6, 4, 8, 3, 7, 6, 0, 1, 5, 9, 5, 0, 7, 3, 0, 8, 9, 4, 3, 2, 8, 3, 2, 7, 4, 9, 5, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A195284 for definitions and a general discussion. LINKS EXAMPLE (A)=6.0609152673132644948643802466... MATHEMATICA a = 7; b = 24; c = 25; 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) A195290 *) 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)=7.5 *) 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) A010524 *) (f1 + f2 + f3)/(a + b + c) RealDigits[%, 10, 100] (* Philo(ABC, I) A195292 *) CROSSREFS Cf. A195284, A195292. Sequence in context: A303494 A198368 A064373 * A280692 A161419 A136526 Adjacent sequences:  A195287 A195288 A195289 * A195291 A195292 A195293 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 14 2011 STATUS approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)