A046095 - OEIS

%I #40 Oct 02 2023 02:38:29

%S 1,5,5,1,3,8,7,5,2,4,5,4,8,3,2,0,3,9,2,2,6,1,9,5,2,5,1,0,2,6,4,6,2,3,

%T 8,1,5,1,6,3,5,9,1,7,0,3,8,0,3,8,8,7,1,9,9,5,2,8,0,0,7,1,2,0,1,1,7,9,

%U 2,6,7,4,2,5,5,4,2,5,6,9,5,7,2,9,5,7,6,0,4,5,3,6,1,2,0,2,5,4,3,6,2,9

%N Decimal expansion of Calabi's constant.

%C An algebraic number of degree 3. - _Charles R Greathouse IV_, Oct 31 2014

%C Named after the Italian-American mathematician Eugenio Calabi (1923-2023). - _Amiram Eldar_, Jun 18 2021

%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 John E. Wetzel, <a href="https://www.jstor.org/stable/3621570">Squares in Triangles</a>, The Mathematical Gazette, Vol. 86, No. 505 (2002), pp. 28-34.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Calabi_triangle">Calabi triangle</a>.

%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>

%F Equals (28*c+2)/sqrt(196*c^2+28*c+145) where c = cos(arctan(12*sqrt(237)/289)/3). - _Robert FERREOL_, Jun 22 2019

%t RealDigits[ x /. FindRoot[ 2x^3-2x^2-3x+2==0, {x, 1.5}, WorkingPrecision->200 ], 10 ][ [ 1 ] ]

%t RealDigits[ Root[ 2x^3-2x^2-3x+2, x, 3], 10, 102][[1]] (* _Jean-François Alcover_, Jun 18 2014 *)

%o (PARI) polrootsreal(2*x^3-2*x^2-3*x+2)[3] \\ _Charles R Greathouse IV_, Oct 31 2014

%Y Cf. A046096.

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_