A195292 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 7,24,25 right triangle ABC.

3, 9, 3, 6, 8, 2, 0, 8, 2, 8, 8, 4, 8, 5, 4, 1, 9, 2, 6, 3, 7, 0, 4, 4, 8, 6, 7, 7, 1, 1, 9, 8, 5, 3, 6, 1, 3, 6, 9, 9, 3, 9, 7, 3, 2, 2, 1, 2, 0, 9, 2, 5, 0, 3, 2, 3, 6, 5, 3, 3, 0, 1, 3, 1, 0, 0, 3, 3, 8, 6, 1, 8, 4, 9, 3, 0, 4, 0, 0, 6, 8, 3, 6, 0, 2, 7, 5, 2, 6, 1, 4, 0, 7, 1, 1, 7, 8, 3, 9, 8

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=0..99.

Example

Philo(ABC,I)=0.39368208288485419263704486771198536...

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.

Sequence in context: A074959 A010632 A340036 * A197572 A224233 A021258

Adjacent sequences: A195289 A195290 A195291 * A195293 A195294 A195295

Keyword

nonn,cons

Author

Clark Kimberling, Sep 14 2011

Status

approved