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A195290 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(7,24,25). 3
6, 0, 6, 0, 9, 1, 5, 2, 6, 7, 3, 1, 3, 2, 6, 4, 4, 9, 4, 8, 6, 4, 3, 8, 0, 2, 4, 6, 6, 1, 2, 9, 9, 1, 7, 6, 5, 2, 9, 8, 5, 9, 3, 7, 5, 1, 6, 1, 5, 4, 9, 1, 7, 4, 2, 1, 8, 5, 7, 7, 0, 3, 0, 5, 6, 7, 4, 5, 6, 7, 7, 6, 4, 8, 3, 7, 6, 0, 1, 5, 9, 5, 0, 7, 3, 0, 8, 9, 4, 3, 2, 8, 3, 2, 7, 4, 9, 5, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

(A)=6.0609152673132644948643802466...

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, A195292.

Sequence in context: A303494 A198368 A064373 * A280692 A161419 A136526

Adjacent sequences:  A195287 A195288 A195289 * A195291 A195292 A195293

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 14 2011

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)