cp's OEIS Frontend

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.

A227472 Decimal expansion of the side of the equilateral triangle that can cover every triangle of perimeter 2.

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%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