This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227472 #19 Feb 13 2025 03:59:02 %S A227472 1,0,0,2,8,5,1,4,2,6,6,3,4,1,8,0,6,6,3,0,4,0,6,1,3,9,9,7,6,4,5,5,0,3, %T A227472 0,3,3,1,0,4,9,7,8,6,3,1,2,3,9,0,3,2,3,1,4,0,0,3,5,0,1,2,1,6,3,0,3,4, %U A227472 6,7,6,7,1,8,1,4,5,2,8,5,5,3,3,4,2,3,5,2,5,0,3,4,7,3,7,8,6,0,1,3 %N A227472 Decimal expansion of the side of the equilateral triangle that can cover every triangle of perimeter 2. %C A227472 Curiously, this side is not 1, as intuitively expected, but a little greater than 1. %D A227472 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 494. %H A227472 John E. Wetzel, <a href="http://www.jstor.org/stable/2691434">The Smallest Equilateral Cover for Triangles of Perimeter Two</a>, Mathematics Magazine Vol. 70, No. 2 (Apr., 1997), pp. 125-130. %F A227472 2/f(x0) where x0 is the global minimum of the trigonometric function f(x) = sqrt(3)*(1+sin(x/2))*sec(Pi/6-x) on the interval [0, Pi/6]. %e A227472 1.00285142663418066304061399764550303310497863123903231400350121630346767... %t A227472 f[x_] := Sqrt[3]*(1 + Sin[x/2])*Sec[Pi/6 - x]; x0 = x /. ToRules @ Reduce[0 < x < Pi/6 && f'[x] == 0, x, Reals]; RealDigits[2/f[x0], 10, 105][[1, 1 ;; 100]] (* _Jean-François Alcover_, Jul 16 2013 *) %o A227472 (PARI) t=solve(x=0,Pi/6, cos(x/2) - 2*(sin(x/2) + 1)*tan(Pi/6 - x)); 4*sin(Pi/6-t)/sqrt(3)/cos(t/2) \\ _Charles R Greathouse IV_, Feb 13 2025 %K A227472 nonn,cons %O A227472 1,4 %A A227472 _Jean-François Alcover_, Jul 16 2013