A195293 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)=(8,15,17).

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

Offset

1,1

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=1..99.

Example

(A)=6.18465843842649082473211478396111...

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, A010524, A195296, A195297.

Sequence in context: A244692 A248589 A288493 * A230763 A371938 A145314

Adjacent sequences: A195290 A195291 A195292 * A195294 A195295 A195296

Keyword

nonn,cons

Author

Clark Kimberling, Sep 14 2011

Status

approved