cp's OEIS Frontend

A195480 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,sqrt(5),3).

%I A195480 #5 Mar 30 2012 18:57:47
%S A195480 1,9,9,5,8,6,7,2,4,7,8,9,6,3,9,1,3,9,0,9,8,1,6,3,6,0,0,6,7,8,2,6,5,0,
%T A195480 4,1,5,8,1,1,5,7,4,4,8,7,2,2,1,5,9,4,7,8,1,0,0,0,3,0,2,0,0,2,1,7,3,1,
%U A195480 6,3,9,8,4,2,4,8,7,8,1,9,7,8,8,4,2,1,1,1,5,7,8,0,4,1,3,3,4,2,7,2
%N A195480 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,sqrt(5),3).
%C A195480 See A195304 for definitions and a general discussion.
%e A195480 (B)=1.99586724789639139098163600678265041581157...
%t A195480 a = 2; b = Sqrt[5]; h = 2 a/3; k = b/3;
%t A195480 f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
%t A195480 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195480 f1 = (f[t])^(1/2) /. Part[s, 4]
%t A195480 RealDigits[%, 10, 100] (* (A) A195479 *)
%t A195480 f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
%t A195480 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195480 f2 = (f[t])^(1/2) /. Part[s, 4]
%t A195480 RealDigits[%, 10, 100] (* (B) A195480 *)
%t A195480 f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
%t A195480 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195480 f3 = (f[t])^(1/2) /. Part[s, 1]
%t A195480 RealDigits[%, 10, 100] (* (C) A195481 *)
%t A195480 c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
%t A195480 RealDigits[%, 10, 100] (* Philo(ABC,G) A195482 *)
%Y A195480 Cf. A195304.
%K A195480 nonn,cons
%O A195480 1,2
%A A195480 _Clark Kimberling_, Sep 19 2011