A104954 - OEIS

%I #19 Feb 16 2025 08:32:57

%S 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,

%T 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,

%U 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

%N Decimal expansion of the area of the regular triangle with circumradius 1.

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

%H Eric Weisstein et al., <a href="https://mathworld.wolfram.com/RootofUnity.html">Root of Unity</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/deMoivreNumber.html">de Moivre Number</a>.

%H I. J. Zucker and G. S. Joyce, <a href="https://doi.org/10.1017/S0305004101005254">Special values of the hypergeometric series II</a>, Math. Proc. Camb. Phil. Soc. 131 (2001) 309-319.

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%F Equals 3*sqrt(3)/4.

%F Equals (1/2)*A104956.

%F Equals 2F1(1/6,1/3 ; 1/2 ; 25/27). [Zucker] - _R. J. Mathar_, Jun 24 2024

%e 1.299038105676657970145584756129404275207103940357785471...

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

%Y Cf. A104955, A104956, A104957.

%K nonn,cons

%O 1,2

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

%E Edited by _Georg Fischer_, Jul 29 2021