A120683 Decimal expansion of secant of 15 degrees (cosecant of 75 degrees).

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

Offset: 1

Author

Rick L. Shepherd, Jun 24 2006

Keywords

• cons
• easy
• nonn
• changed

Comments

Side length of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link).

A quartic integer. - Charles R Greathouse IV, Aug 27 2017

Examples

			1.03527618041008304939559535049619331339627560527972...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.2, p. 487.

Links

• Eric Weisstein's World of Mathematics, Equilateral Triangle.
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A002193, A019679, A019691, A019884, A010464, A092242, A101263.

Programs

Mathematica

RealDigits[Sec[15 Degree],10,120][[1]] (* Harvey P. Dale, Jun 03 2015 *)

PARI

sqrt(6) - sqrt(2) \\ Charles R Greathouse IV, Aug 27 2017

Formula

Equals sec(Pi/12) = sec(A019679) = sqrt(6) - sqrt(2) = A010464 - A002193 = csc(5*Pi/12) = 1/sin(5*Pi/12) = 1/sin(10*A019691) = 1/A019884.

Equals Product_{k >= 1} 1/(1 - 1/(36*(2*k - 1)^2)). - Antonio Graciá Llorente, Mar 20 2024

From Amiram Eldar, Nov 24 2024: (Start)

Equals 2*A101263.

Equals Product_{k>=1} (1 - (-1)^k/A092242(k)). (End)

Smallest positive of the 4 real-valued roots of x^4-16*x^2+16=0. - R. J. Mathar, Aug 31 2025