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 A195297 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of an 8,15,17 right triangle ABC. 4
 5, 4, 1, 6, 7, 7, 0, 5, 2, 1, 6, 1, 9, 8, 5, 5, 4, 2, 0, 6, 4, 7, 8, 0, 7, 6, 4, 5, 5, 6, 8, 5, 0, 0, 9, 2, 5, 2, 4, 1, 1, 2, 7, 0, 2, 3, 0, 4, 6, 3, 2, 1, 3, 5, 8, 9, 9, 9, 5, 0, 9, 2, 2, 0, 3, 5, 7, 0, 4, 9, 6, 1, 6, 1, 6, 8, 7, 8, 2, 4, 4, 4, 1, 7, 0, 6, 0, 2, 2, 6, 8, 4, 8, 1, 3, 7, 9, 5, 8, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A195284 for definitions and a general discussion. LINKS EXAMPLE Philo(ABC,I)=0.54167705216198554206478076455685009252411270... MATHEMATICA a = 8; b = 15; c = 17; 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) A195293 *) 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) A195296 *) 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), A195297 *) CROSSREFS Cf. A195284. Sequence in context: A084129 A011503 A296498 * A336284 A258639 A072222 Adjacent sequences:  A195294 A195295 A195296 * A195298 A195299 A195300 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 14 2011 STATUS approved

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Last modified August 11 03:07 EDT 2020. Contains 336421 sequences. (Running on oeis4.)