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 A192408 #48 Feb 16 2025 08:33:15
%S A192408 2,6,4,9,3,2,0,8,4,6,0,2,7,7,6,8,6,2,4,3,4,1,1,6,4,9,4,7,6,2,5,7,1,0,
%T A192408 6,8,6,5,0,1,9,0,0,6,6,0,4,1,3,6,4,4,5,2,8,7,8,7,4,4,8,9,3,2,9,2,0,9,
%U A192408 0,2,5,0,8,7,0,6,8,8,6,3,8,9,7,2,7,3,4,9,8,5,2,3,3,7,4,6,1,8,4,4
%N A192408 Decimal expansion of the solution to x = sin( Pi/6 - x*sqrt(1 - x^2) ).
%C A192408 Trisecting an ellipse area.
%C A192408 Given the ellipse x^2/a^2 + y^2/b^2 = 1, one way to trisect its area is to use the symmetric lines x = s and x = -s, s being the unique real solution to s = a*sin(Pi/6 - (s*sqrt(a^2 - s^2))/a^2).
%C A192408 Setting s = a * t, the equation in t becomes t = sin( Pi/6 - t*sqrt(1 - t^2) ), which is noticeably independent of eccentricity.
%C A192408 In the case of a unit radius circle, total cut length is 4*sqrt(1-t^2) = 3.857068297..., which is quite larger than cutting along 3 radii.
%C A192408 This constant is also the solution to an elementary problem involving two overlapping circles, known as "Mrs. Miniver's problem" (cf. S. R. Finch, p. 487). The distance between the centers of the two circles is 2*x = 0.5298641692...
%D A192408 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 487.
%H A192408 L. A. Graham, <a href="/A192408/a192408.gif">Mrs Miniver's problem</a>, Ingenious Mathematical Problems and Methods, Dover, 1959, p. 6.
%H A192408 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ellipse.html">Ellipse</a>.
%e A192408 0.26493208460277686243411649476257106865019006604136445287874489329209025087...
%t A192408 RealDigits[ x /. FindRoot[x == Sin[Pi/6 - x*Sqrt[1 - x^2]], {x, 1/4}, WorkingPrecision -> 100]][[1]]
%o A192408 (PARI) solve(x=.2,.3,sin(Pi/6-x*sqrt(1-x^2))-x) \\ _Charles R Greathouse IV_, Jun 30 2011
%o A192408 (PARI) sin(solve(x=0,1,sin(x)+x-Pi/3)/2) \\ _Gleb Koloskov_, Aug 25 2021
%K A192408 nonn,cons
%O A192408 0,1
%A A192408 _Jean-François Alcover_, Jun 30 2011