A195451 Decimal expansion of shortest length, (B), of segment from side BC through centroid to side BA in right triangle ABC with sidelengths (a,b,c)=(2,3,sqrt(13)).

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

Offset

1,1

Comments

See A195304 for definitions and a general discussion.

Links

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

Example

(B)=2.3411607930733219756148533813763834934244253886784...

Mathematica

a = 2; b = 3; h = 2 a/3; k = b/3;
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) A195450 *)
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] (* (B) A195451 *)
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] (* (C) A195452  *)
c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
RealDigits[%, 10, 100] (* Philo(ABC, G) A195453 *)

Crossrefs

Cf. A195304.

Sequence in context: A190594 A338803 A104412 * A298160 A118310 A073057

Adjacent sequences: A195448 A195449 A195450 * A195452 A195453 A195454

Keyword

nonn,cons

Author

Clark Kimberling, Sep 18 2011

Status

approved