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A195285 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 3,4,5 right triangle ABC. 2
5, 9, 7, 7, 2, 3, 3, 5, 0, 7, 5, 2, 0, 7, 4, 9, 4, 5, 7, 2, 3, 2, 0, 6, 6, 7, 8, 8, 9, 7, 7, 0, 7, 0, 6, 2, 3, 6, 6, 0, 8, 3, 2, 3, 9, 1, 5, 9, 6, 3, 0, 5, 3, 5, 1, 5, 5, 2, 1, 6, 1, 0, 7, 4, 9, 3, 3, 6, 5, 1, 8, 1, 2, 4, 9, 0, 1, 4, 8, 1, 5, 9, 4, 5, 3, 9, 0, 6, 8, 4, 6, 6, 2, 7, 9, 9, 9, 1, 2, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A195285 for a definition of Philo(ABC,I) and general discussion.

LINKS

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

EXAMPLE

Philo(ABC,I)=0.59772335075207494572...

MATHEMATICA

a = 3; b = 4; c = 5;

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) 195284 *)

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 A002163 *)

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) A010466 *)

(f1 + f2 + f3)/(a + b + c)

RealDigits[%, 10, 100] (* Philo(ABC, I) A195285 *)

CROSSREFS

Cf. A195284.

Sequence in context: A125650 A171540 A220261 * A200597 A140724 A086055

Adjacent sequences:  A195282 A195283 A195284 * A195286 A195287 A195288

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 14 2011

STATUS

approved

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)