A343054 Decimal expansion of the imaginary part of i^(1/12), or sin(Pi/24).

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

Offset: 0

Author

Seiichi Manyama, Apr 04 2021

Keywords

• nonn
• cons
• easy
• changed

Examples

			0.130526192220051591548...
		

Links

• Wikipedia, Trigonometric constants expressed in real radicals
• Index entries for algebraic numbers, degree 8

Crossrefs

Cf. A144982 (cos(Pi/24)).

Programs

Mathematica

RealDigits[Sin[Pi/24], 10, 100][[1]] (* Amiram Eldar, Apr 27 2021 *)

PARI

imag(I^(1/12))

PARI

sin(Pi/24)

PARI

sqrt(2-sqrt(2+sqrt(3)))/2

Formula

Equals (1/2) * sqrt(2-sqrt(2+sqrt(3))).

This^2 + A144982^2 = 1. - R. J. Mathar, Aug 31 2025

Smallest positive root of 256*x^8-512*x^6+320*x^4-64*x^2+1=0. - R. J. Mathar, Aug 31 2025