A362922 Decimal expansion of cos(2*Pi/7) = sin(3*Pi/14) = A255249/2.

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

Offset: 0

Author

N. J. A. Sloane, Jun 25 2023

Keywords

• nonn
• cons

Comments

This number, negated, is a zero of the polynomial 8*x^3 - 4*x^2 - 4*x + 1 that arises in the dissection of a regular heptagon. The other two zeros are cos(Pi/7) (A073052) and sin(Pi/14) (A232736).

The old definition was: Decimal expansion of 1/(8*cos(Pi/7)*sin(Pi/14)).

Examples

			0.6234898018587335305250048840042398106322747308964021053655...
		

Crossrefs

Cf. A073052, A160389, A232736, A255249.

Programs

Maple

Digits := 110: evalf(((-1)^(2/7) - (-1)^(5/7))/2, Digits)*10^96:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Jun 25 2023

Mathematica

First@ RealDigits[1/(8*Cos[Pi/7]*Sin[Pi/14]), 10, 96] (* Michael De Vlieger, Jun 25 2023 *)

Formula

Equals 1/(4*cos(Pi/7)-2) = 1/(2*A160389-2). - Alois P. Heinz, Jun 25 2023

Equals (i^(4/7) - i^(10/7))/2. - Peter Luschny, Jun 26 2023

Extensions

Simpler definition from Alois P. Heinz, Jun 25 2023.