cp's OEIS Frontend

A195476 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)=(1,sqrt(3),2).

%I A195476 #5 Mar 30 2012 18:57:45
%S A195476 1,2,7,2,2,2,4,6,5,6,0,9,0,3,5,2,3,3,6,6,0,8,1,4,1,9,8,1,3,6,9,2,1,8,
%T A195476 6,0,9,5,4,9,2,0,7,5,8,8,9,4,2,5,6,3,3,0,6,9,5,6,9,4,3,5,5,8,7,1,3,6,
%U A195476 7,4,5,3,7,4,5,2,9,4,1,8,2,3,6,0,9,7,8,6,3,3,3,5,0,1,1,8,1,8,3,5
%N A195476 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)=(1,sqrt(3),2).
%C A195476 See A195304 for definitions and a general discussion.
%e A195476 (B)=1.272224656090352336608141981369218609549207...
%t A195476 a = 1; b = Sqrt[3]; h = 2 a/3; k = b/3;
%t A195476 f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
%t A195476 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195476 f1 = (f[t])^(1/2) /. Part[s, 4]
%t A195476 RealDigits[%, 10, 100] (* (A) A195575 *)
%t A195476 f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
%t A195476 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195476 f2 = (f[t])^(1/2) /. Part[s, 4]
%t A195476 RealDigits[%, 10, 100] (* (B) A195576 *)
%t A195476 f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
%t A195476 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195476 f3 = (f[t])^(1/2) /. Part[s, 4]
%t A195476 RealDigits[%, 10, 100] (* (C) A195577 *)
%t A195476 c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
%t A195476 RealDigits[%, 10, 100] (* Philo(ABC,G) A195578 *)
%Y A195476 Cf. A195304.
%K A195476 nonn,cons
%O A195476 1,2
%A A195476 _Clark Kimberling_, Sep 19 2011