cp's OEIS Frontend

A195427 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)=(7,24,25).

%I A195427 #5 Mar 30 2012 18:57:45
%S A195427 1,2,2,2,2,4,4,4,2,3,2,2,5,9,6,9,8,0,5,1,3,3,2,5,9,6,3,6,3,2,5,9,7,9,
%T A195427 7,9,3,1,2,0,8,2,0,5,9,2,3,8,6,3,6,7,9,5,7,6,4,6,8,9,2,4,2,6,6,4,9,6,
%U A195427 6,3,4,6,2,0,7,7,2,0,8,7,9,0,4,1,4,8,0,4,8,3,2,3,8,8,1,7,7,6,2,1
%N A195427 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)=(7,24,25).
%C A195427 See A195304 for definitions and a general discussion.
%e A195427 (C)=12.22244423225969805133259636325979793120...
%t A195427 a = 7; b = 24; h = 2 a/3; k = b/3;
%t A195427 f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2
%t A195427 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195427 f1 = (f[t])^(1/2) /. Part[s, 4]
%t A195427 RealDigits[%, 10, 100] (* (A) A195425 *)
%t A195427 f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2
%t A195427 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195427 f2 = (f[t])^(1/2) /. Part[s, 4]
%t A195427 RealDigits[%, 10, 100] (* (B) A195426 *)
%t A195427 f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2
%t A195427 s = NSolve[D[f[t], t] == 0, t, 150]
%t A195427 f3 = (f[t])^(1/2) /. Part[s, 1]
%t A195427 RealDigits[%, 10, 100] (* (C) A195427 *)
%t A195427 c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)
%t A195427 RealDigits[%, 10, 100] (* Philo(ABC,G) A195428 *)
%Y A195427 Cf. A195304.
%K A195427 nonn,cons
%O A195427 2,2
%A A195427 _Clark Kimberling_, Sep 18 2011