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

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