A104954 Decimal expansion of the area of the regular triangle with circumradius 1.

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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 30 2005

Keywords

• nonn
• cons

Comments

Equivalently, the area in the complex plane of the smallest convex set containing all order-3 roots of unity.

Examples

			1.299038105676657970145584756129404275207103940357785471...
		

Links

• Eric Weisstein et al., Root of Unity.
• Eric Weisstein's World of Mathematics, de Moivre Number.
• I. J. Zucker and G. S. Joyce, Special values of the hypergeometric series II, Math. Proc. Camb. Phil. Soc. 131 (2001) 309-319.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A104955, A104956, A104957.

Programs

Mathematica

RealDigits[N[Floor[n/2]*Sin[(2*Pi)/n] - Sin[(4*Pi*Floor[n/2])/n]/2 /. n -> 3, 108]][[1]]

Formula

Equals 3*sqrt(3)/4.

Equals (1/2)*A104956.

Equals 2F1(1/6,1/3 ; 1/2 ; 25/27). [Zucker] - R. J. Mathar, Jun 24 2024

Extensions

Edited by Georg Fischer, Jul 29 2021