A046095 Decimal expansion of Calabi's constant.

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, 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, 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

Offset

1,2

Comments

An algebraic number of degree 3. - Charles R Greathouse IV, Oct 31 2014

Named after the Italian-American mathematician Eugenio Calabi (1923-2023). - Amiram Eldar, Jun 18 2021

References

John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus (Springer-Verlag), 1996, p. 206.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 8.13, pp. 523-524.

Links

Table of n, a(n) for n=1..102.

Eugenio Calabi, Outline of Proof Regarding Squares Wedged in Triangle, 1997.

Eric Weisstein's World of Mathematics, Calabi's Triangle.

John E. Wetzel, Squares in Triangles, The Mathematical Gazette, Vol. 86, No. 505 (2002), pp. 28-34.

Wikipedia, Calabi triangle.

Index entries for algebraic numbers, degree 3

Formula

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

Mathematica

RealDigits[ x /. FindRoot[ 2x^3-2x^2-3x+2==0, {x, 1.5}, WorkingPrecision->200 ], 10 ][ [ 1 ] ]
RealDigits[ Root[ 2x^3-2x^2-3x+2, x, 3], 10, 102][[1]] (* Jean-François Alcover, Jun 18 2014 *)

Prog

(PARI) polrootsreal(2*x^3-2*x^2-3*x+2)[3] \\ Charles R Greathouse IV, Oct 31 2014

Crossrefs

Cf. A046096.

Sequence in context: A145227 A236555 A282969 * A322545 A256737 A055183

Adjacent sequences: A046092 A046093 A046094 * A046096 A046097 A046098

Keyword

nonn,cons

Author

Eric W. Weisstein

Status

approved