cp's OEIS Frontend

A195430 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)=(8,15,17).

%I A195430 #5 Mar 30 2012 18:57:45
%S A195430 1,0,6,7,1,1,6,5,0,3,6,7,1,3,5,9,4,3,5,0,4,0,6,6,1,9,1,8,2,1,2,5,9,6,
%T A195430 0,2,6,8,7,8,6,6,7,0,4,4,8,6,1,3,2,0,4,4,4,6,5,3,9,1,7,8,9,4,6,0,7,8,
%U A195430 6,0,5,1,2,1,4,6,9,3,4,5,5,7,5,6,2,3,1,7,9,8,4,7,6,0,2,9,4,6,3,4
%N A195430 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)=(8,15,17).
%C A195430 See A195304 for definitions and a general discussion.
%e A195430 (B)=10.6711650367135943504066191821259602...
%t A195430 a = 8; b = 15; h = 2 a/3; k = b/3;
%t A195430 f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
%t A195430 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195430 f1 = (f[t])^(1/2) /. Part[s, 4]
%t A195430 RealDigits[%, 10, 100] (* (A) A195429 *)
%t A195430 f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
%t A195430 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195430 f2 = (f[t])^(1/2) /. Part[s, 4]
%t A195430 RealDigits[%, 10, 100] (* (B) A195430 *)
%t A195430 f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
%t A195430 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195430 f3 = (f[t])^(1/2) /. Part[s, 1]
%t A195430 RealDigits[%, 10, 100] (* (C) A195431 *)
%t A195430 c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
%t A195430 RealDigits[%, 10, 100] (* Philo(ABC,G) A195432 *)
%Y A195430 Cf. A195304.
%K A195430 nonn,cons
%O A195430 2,3
%A A195430 _Clark Kimberling_, Sep 18 2011