|
%I #56 Jun 18 2021 21:58:44
%S 1,7,7,5,6,2,7,2,5,5,2,6,9,6,2,9,8,6,2,5,0,8,4,8,1,6,7,2,0,2,8,7,2,8,
%T 5,4,2,6,9,5,0,9,1,7,6,5,5,6,8,6,6,9,3,4,4,7,9,2,3,8,1,4,1,9,8,1,0,3,
%U 1,5,2,6,5,9,8,5,3,3,9,9,9,7,9,2,0,1,3
%N Decimal expansion of the angle in radians at the apex of the Calabi triangle.
%C The angle in degrees is 101.7359477153... and each of the base angles is 0.6829826991... radians or 39.1320261423... degrees.
%D John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus (Springer-Verlag), 1996, p. 206.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 8.13, pp. 523-524.
%H Eugenio Calabi, <a href="https://web.archive.org/web/20140903140348/http://www.people.fas.harvard.edu/~sfinch/csolve/calabi.html">Outline of Proof Regarding Squares Wedged in Triangle</a>, 1997.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CalabisTriangle.html">Calabi's Triangle</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Calabi_triangle">Calabi triangle</a>.
%F Equals 2*arcsin(c/2), where c = A046095.
%e 1.77562725526962986250848167202872854269509176556866...
%t r = x /. FindRoot[2 x^3 - 2 x^2 - 3 x + 2 == 0, {x, 1.5}, WorkingPrecision -> 200]; RealDigits[2*ArcSin[r/2], 10, 100][[1]]
%Y Cf. A046095.
%K nonn,cons
%O 1,2
%A _Amiram Eldar_, Jun 18 2021
|
