A120683 - OEIS

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

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OFFSET

1,3

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Equilateral Triangle.

Index entries for algebraic numbers, degree 4.

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)

EXAMPLE

1.03527618041008304939559535049619331339627560527972...