AUTHOR
_Clark Kimberling (ck6(AT)evansville.edu), _, Sep 14 2011
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_Clark Kimberling (ck6(AT)evansville.edu), _, Sep 14 2011
proposed
approved
editing
proposed
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) A010487 *)
RealDigits[%, 10, 100] (* (CB) A195288 *)
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) A010487 *)
RealDigits[%, 10, 100] (* Philo(A, B, C, I) A195289 *)
approved
editing
editing
approved
proposed
approved
editing
proposed
allocated for Clark KimberlingDecimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 3,4,5 right triangle ABC.
4, 8, 4, 7, 8, 2, 3, 8, 5, 3, 6, 6, 1, 7, 5, 3, 4, 8, 3, 3, 5, 1, 6, 5, 4, 1, 8, 0, 2, 2, 8, 1, 1, 5, 2, 7, 8, 0, 8, 8, 2, 5, 5, 4, 5, 2, 2, 8, 2, 5, 9, 9, 2, 3, 4, 1, 2, 9, 5, 4, 4, 3, 3, 4, 6, 0, 2, 1, 8, 8, 6, 9, 4, 6, 2, 9, 6, 2, 9, 3, 6, 8, 4, 9, 2, 7, 9, 5, 9, 9, 8, 0, 7, 0, 1, 2, 2, 0, 6, 2
0,1
See A195284 for definitions and a general discussion.
Philo(ABC,I)=0.4847823853661753483351654180...
a = 5; b = 12; c = 13;
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) A195286 *)
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) A195287 *)
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) A195288 *)
(f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(A, B, C, I) *)
allocated
nonn,cons
Clark Kimberling (ck6(AT)evansville.edu), Sep 14 2011
approved
editing