A195288 - OEIS

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A195288

Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(5,12,13).

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

(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

(C)=4.80740170061865239082562835...

MATHEMATICA

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_] := (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) 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 *)

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

RealDigits[%, 10, 100] (* Philo(A, B, C, I) A195289 *)

CROSSREFS

Cf. A195284.

Sequence in context: A199777 A200389 A195455 * A251992 A021212 A197284

Adjacent sequences: A195285 A195286 A195287 * A195289 A195290 A195291

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 14 2011

STATUS

approved