cp's OEIS Frontend

A195481 Decimal expansion of shortest length, (C), of segment from side CA through centroid to side CB in right triangle ABC with sidelengths (a,b,c)=(2,sqrt(5),3).

%I A195481 #5 Mar 30 2012 18:57:47
%S A195481 1,3,5,6,9,1,7,4,0,3,9,3,7,7,6,0,3,6,5,7,9,2,8,0,7,7,5,9,7,6,7,0,7,8,
%T A195481 5,4,9,7,6,1,1,2,8,6,4,0,3,9,0,3,9,1,2,0,2,3,9,6,2,7,2,4,9,7,5,2,9,7,
%U A195481 0,0,4,2,7,4,9,4,9,7,9,5,3,7,5,0,6,9,6,2,0,8,5,1,9,0,4,8,6,4,8,0
%N A195481 Decimal expansion of shortest length, (C), of segment from side CA through centroid to side CB in right triangle ABC with sidelengths (a,b,c)=(2,sqrt(5),3).
%C A195481 See A195304 for definitions and a general discussion.
%e A195481 (C)=1.3569174039377603657928077597670785...
%t A195481 a = 2; b = Sqrt[5]; h = 2 a/3; k = b/3;
%t A195481 f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
%t A195481 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195481 f1 = (f[t])^(1/2) /. Part[s, 4]
%t A195481 RealDigits[%, 10, 100] (* (A) A195479 *)
%t A195481 f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
%t A195481 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195481 f2 = (f[t])^(1/2) /. Part[s, 4]
%t A195481 RealDigits[%, 10, 100] (* (B) A195480 *)
%t A195481 f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
%t A195481 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195481 f3 = (f[t])^(1/2) /. Part[s, 1]
%t A195481 RealDigits[%, 10, 100] (* (C) A195481 *)
%t A195481 c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
%t A195481 RealDigits[%, 10, 100] (* Philo(ABC,G) A195482 *)
%Y A195481 Cf. A195304.
%K A195481 nonn,cons
%O A195481 1,2
%A A195481 _Clark Kimberling_, Sep 19 2011