A195297 - OEIS

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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.

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

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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)=0.54167705216198554206478076455685009252411270...

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