A241243 Decimal representation of sin(Pi/17).

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

Offset: 0

Author

Zak Seidov, Apr 18 2014

Keywords

• nonn
• cons
• changed

Examples

			0.18374951781657033157440883962072758248913852384449940585065085774891492825305...
		

References

• Saul Stahl, "Geometry From Euclid To Knots" Chapter 4.3, 'Regular Polygons', Courier - Dover Publications, NJ, 2009, pp. 153-154.

Links

• Wikipedia, Constructible polygon
• Index entries for algebraic numbers, degree 16

Programs

Maple

Digits:=100: evalf(sin(Pi/17)); # Wesley Ivan Hurt, Aug 15 2014

Mathematica

RealDigits[ Sin[ Pi/17], 10, 111][[1]] (* Robert G. Wilson v, Aug 14 2014 *)
RealDigits[Root[17 - 816 x^2 + 11424 x^4 - 71808 x^6 + 239360 x^8 -
  452608 x^10 + 487424 x^12 - 278528 x^14 + 65536 x^16, 9],10,105][[1]] (* Artur Jasinski, Aug 04 2025 *)

Formula

Equals 1/4 sqrt(8 - sqrt(2*(15 + sqrt(17) - sqrt(2*(17 - sqrt(17))) + sqrt(2*(34 + 6 sqrt(17) + sqrt(2*(17 - sqrt(17))) - sqrt(34*(17 - sqrt(17))) + 8*sqrt(2*(17 + sqrt(17)))))))). - Robert G. Wilson v, Aug 14 2014

The minimal polynomial is 65536x^16 - 278528x^14 + 487424x^12 - 452608x^10 + 2398360x^8 - 71808 x^6 + 11424x^4 - 816x^2 + 17. - Robert G. Wilson v, Aug 14 2014

This^2 + A210649^2 = 1. - R. J. Mathar, Aug 31 2025

Extensions

Offset corrected by Amiram Eldar, Aug 04 2025