A019879 -id:A019879 - cp's OEIS frontend

A019819 Decimal expansion of sine of 10 degrees.

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

Offset: 0

N. J. A. Sloane

Also the imaginary part of i^(1/9). - Stanislav Sykora, Apr 25 2012

			0.173648177...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Vladimir Ivanovich Smirnov, A course of higher mathematics, vol. 1 , Pergamon Press, 1964, p. 342.
Index entries for algebraic numbers, degree 3.

Cf. A019814.

First[RealDigits[Root[1 - 6 #1 + 8 #1^3 &, 2], 10, 100]] (* Artur Jasinski, Oct 28 2008 *)
RealDigits[ Sin[Pi/18], 10, 111]  (* Robert G. Wilson v *)

sin(Pi/18) \\ Charles R Greathouse IV, Apr 25 2012

Equals cos(4*Pi/9) = 2F1(7/6,-1/6;1/2;3/4) / 2 = - 2F1(4/3,-1/3;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
From Artur Jasinski, Oct 28 2008: (Start)
Decimal expansion of root of cubic polynomial 1 - 6*x + 8*x^3. (Others A019859, -A019879)
Decimal expansion of casus irreducibilis:
(1/2) * (((-i*sqrt(3) - 1)/2)^(2/3) + ((i*sqrt(3) - 1)/2)^(2/3)). (End)
Equals 2 * A019814 * A019894. - R. J. Mathar, Jan 17 2021
This^2 + A019889^2 = 1. - R. J. Mathar, Aug 31 2025

A144981 Decimal expansion of cos(Pi/8) = cos(22.5 degrees).

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Sep 28 2008

Also the real part of i^(1/4). - Stanislav Sykora, Apr 25 2012
Width of a regular octagon of unit diameter. See Bingane and Audet. - Michel Marcus, Oct 04 2021
Minimal polynomial 8x^4 - 8x^2 + 1. - Charles R Greathouse IV, Oct 30 2023
Also the ratio (1+sqrt(2))/sqrt(4+2*sqrt(2)) of the radii and perimeters of the inscribed and circumscribed circles of a regular octagon. This and the first two comments are actually all equivalent. - M. F. Hasler, Aug 13 2025

			Equals 0.923879532511286756128183189396788286822416625863642486115097...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Christian Bingane and Charles Audet, The equilateral small octagon of maximal width, arXiv:2110.00036 [math.MG], 2021.
Wikipedia, Exact trigonometric constants.
Wikipedia, Octagon.
Index entries for algebraic numbers, degree 4

Cf. A019863: cos(Pi/5), A010527: cos(Pi/6), A073052: cos(Pi/7), A019879: cos(Pi/9).

Maple
```
evalf(sqrt(2+sqrt(2))/2) ;
```

RealDigits[ Sqrt[2 + Sqrt[2]]/2, 10, 111][[1]] (* Or *) RealDigits[ Cos[Pi/8], 10, 111][[1]] (* Robert G. Wilson v *)

cos(Pi/8) \\ Michel Marcus, Dec 15 2015

from math import isqrt # integer arithmetic, avoiding 10^(4N) in inner isqrt
def A144981_first(N=99): return [9] if N<2 else list(map(int,str(
    isqrt(isqrt(100**(N+2)>>3)*10**(N-2)+100**N//2)))) # M. F. Hasler, Aug 13 2025

numerical_approx(sqrt(2+sqrt(2))/2, digits=120) # G. C. Greubel, Sep 04 2022

Equals sqrt(2 + sqrt(2))/2 = sqrt(3.41421...)/2 = 1.8477759.../2.
Equals Hypergeometric2F1([11/16, 5/16], [1/2], 3/4) / 2. - R. J. Mathar, Oct 27 2008
Equals 2F1(-1/4,1/4;1/2;1/2) . - R. J. Mathar, Aug 31 2025

A019829 Decimal expansion of sine of 20 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

			0.34202014332566873304409961468225958076308336751416062846504849768471476...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 6

Cf. A323601.

RealDigits[ Sin[Pi/9], 10, 111][[1]]  (* Robert G. Wilson v *)

/* for x = 20 degrees, sin(9x) = 0 */
/* so sin(x) is a zero of this polynomial */
sin_9(x)=9*x-120*x^3+432*x^5-576*x^7+256*x^9
x=34;y=100;print(3);print(4);
for(digits=1, 110, {d=0;y=y*10;while(sin_9((10*x+d)/y) > 0, d++);
d--; /* while loop overshoots correct digit */
print(d); x=10*x+d})
\\ Michael B. Porter, Jan 27 2010

sin(Pi/9) \\ Charles R Greathouse IV, Feb 04 2025

Equals cos(7*Pi/18) = 2F1(13/12,-1/12;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
Root of the equation 64*x^6 - 96*x^4 + 36*x^2 - 3 = 0. - Vaclav Kotesovec, Jan 19 2019 (other A019849, A019889)
Equals sqrt(8 - 2^(4/3)*(1 + i*sqrt(3))^(2/3) + i*2^(2/3)*(1 + i*sqrt(3))^(1/3)*(i + sqrt(3)))/4, where i is the imaginary unit. - Vaclav Kotesovec, Jan 19 2019
Equals 2*A019819 *A019889. - R. J. Mathar, Jan 17 2021
This^2 + A019879^2=1. - R. J. Mathar, Aug 31 2025

A332437 Decimal expansion of 2*cos(Pi/9).

Original entry on oeis.org

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

Offset: 1

Wolfdieter Lang, Mar 27 2020

This algebraic number called rho(9) of degree 3 = A055034(9) has minimal polynomial C(9, x) = x^3 - 3*x - 1 (see A187360).
rho(9) gives the length ratio diagonal/side of the smallest diagonal in the regular 9-gon.
The length ratio diagonal/side of the second smallest and the third smallest (or the largest) diagonal in the regular 9-gon are rho(9)^2 - 1 = A332438 - 1 and rho(9) + 1, respectively. - Mohammed Yaseen, Oct 31 2020

			rho(9) = 1.87938524157181676810821855464946293987241626852892926618...

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 207.

Index entries for algebraic numbers, degree 3.

Cf. A019879, A055034, A056020, A156638, A187360, A214778, A215885, A332438.

RealDigits[2 * Cos[Pi/9], 10, 100][[1]] (* Amiram Eldar, Mar 27 2020 *)

2*cos(Pi/9) \\ Michel Marcus, Mar 28 2020

rho(9) = 2*cos(Pi/9).
Equals (-1)^(-1/9)*((-1)^(1/9) - i)*((-1)^(1/9) + i). - Peter Luschny, Mar 27 2020
Equals 2*A019879. - Michel Marcus, Mar 28 2020
Equals sqrt(A332438). - Mohammed Yaseen, Oct 31 2020
From Peter Bala, Oct 20 2021: (Start)
The zeros of x^3 - 3*x - 1 are r_1 = -2*cos(2*Pi/9), r_2 = -2*cos(4*Pi/9) and r_3 = -2*cos(8*Pi/9) = 2*cos(Pi/9).
The polynomial x^3 - 3*x - 1 is irreducible over Q (since it is irreducible mod 2) with discriminant equal to 3^4, a square. It follows that the Galois group of the number field Q(2*cos(Pi/9)) over Q is cyclic of order 3.
The mapping r -> 2 - r^2 cyclically permutes the zeros r_1, r_2 and r_3. The inverse cyclic permutation is given by r -> r^2 - r - 2.
The first differences r_1 - r_2, r_2 - r_3 and r_3 - r_1 are the zeros of the cyclic cubic polynomial x^3 - 9*x - 9 of discriminant 3^6.
First quotient relations:
r_1/r_2 = 1 + (r_3 - r_1); r_2/r_3 = 1 + (r_1 - r_2); r_3/r_1 = 1 + (r_2 - r_3);
r_2/r_1 = (r_3 - r_2) - 2; r_3/r_2 = (r_1 - r_3) - 2; r_1/r_3 = (r_2 - r_1) - 2;
r_1/r_2 + r_2/r_3 + r_3/r_1 = 3; r_2/r_1 + r_3/r_2 + r_1/r_3 = -6.
Thus the first quotients r_1/r_2, r_2/r_3 and r_3/r_1 are the zeros of the cyclic cubic polynomial x^3 - 3*x^2 - 6*x - 1 of discriminant 3^6. See A214778.
Second quotient relations:
(r_1*r_2)/(r_3^2) = 3*r_2 - 6*r_1 - 8, with two other similar relations by cyclically permuting the 3 zeros. The three second quotients are the zeros of the cyclic cubic polynomial x^3 + 24*x^2 + 3*x - 1 of discriminant 3^10.
(r_1^2)/(r_2*r_3) = 1 - 3*(r_2 + r_3), with two other similar relations by cyclically permuting the 3 zeros. (End)
Equals i^(2/9) + i^(-2/9). - Gary W. Adamson, Jun 25 2022
Equals Re((4+4*sqrt(3)*i)^(1/3)). - Gerry Martens, Mar 19 2024
From Amiram Eldar, Nov 22 2024: (Start)
Equals Product_{k>=1} (1 - (-1)^k/A056020(k)).
Equals 1 + Product_{k>=1} (1 + (-1)^k/A156638(k)). (End)

A332438 Decimal expansion of (2*cos(Pi/9))^2 = A332437^2.

Original entry on oeis.org

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

Offset: 1

Wolfdieter Lang, Mar 31 2020

This algebraic number rho(9)^2 of degree 3 is a root of its minimal polynomial x^3 - 6*x^2 + 9*x - 1.
The other two roots are x2 = (2*cos(5*Pi/9))^2 = (2*cos(4*Pi/9))^2 = (R(4,rho(9)))^2 = 2 - rho(9) = 0.120614758..., and x3 = (2*cos(7*Pi/9))^2 = (2*cos(7*Pi/9))^2 = (R(7,rho(9)))^2 = 4 + rho(9) - rho(9)^2 = 2.347296355... = A130880 + 2, with rho(9) = 2*cos(Pi/9) = A332437, the monic Chebyshev polynomials R (see A127672), and the computation is done modulo the minimal polynomial of rho(9) which is x^3 - 3*x - 1 (see A187360).
This gives the representation of these roots in the power basis of the simple field extension Q(rho(9)). See the linked W. Lang paper in A187360, sect. 4.
This number rho(9)^2 appears as limit of the quotient of consecutive numbers af various sequences, e.g., A094256 and A094829.
The algebraic number rho(9)^2 - 2 = 1.532088898... of Q(rho(9)) has minimal polynomial x^3 - 3*x + 1 over Q. The other roots are -rho(9) = -A332437 and 2 + rho(9) - rho(9)^2 = A130880. - Wolfdieter Lang, Sep 20 2022

			3.5320888862379560704047853011108333478716649...

Index entries for algebraic numbers, degree 3.

Cf. A019879, A063289, A094256, A094829, A127672, A130880, A187360, A332437.

2 + 2*cos(2*Pi/n): A104457 (n = 5), A116425 (n = 7), A296184 (n = 10), A019973 (n = 12).

RealDigits[(2*Cos[Pi/9])^2, 10, 100][[1]] (* Amiram Eldar, Mar 31 2020 *)

(2*cos(Pi/9))^2 \\ Michel Marcus, Sep 23 2022

Equals (2*cos(Pi/9))^2 = rho(9)^2 = A332437^2.
Equals 2 + i^(4/9) - i^(14/9). - Peter Luschny, Apr 04 2020
Equals 2 + w1^(1/3) + w2^(1/3), where w1 = (-1 + sqrt(3)*i)/2 = exp(2*Pi*i/3) and w2 = (-1 - sqrt(3)*i)/2 are the complex roots of x^3 - 1. - Wolfdieter Lang, Sep 20 2022
Constant c = 2 + 2*cos(2*Pi/9). The linear fractional transformation z -> c - c/z has order 9, that is, z = c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(z))))))))). - Peter Bala, May 09 2024
From Amiram Eldar, Nov 22 2024: (Start)
Equals 3 + sec(Pi/9)/2 = 3 + 1/(2*A019879).
Equals 3 + Product_{k>=3} (1 + (-1)^k/A063289(k)). (End)

A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 01 2024

			1.3737387097273111393808320132488363588759362995854...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Apothem.
Index entries for algebraic numbers, degree 6.

Cf. A375151 (circumradius), A375153 (sagitta), A256853 (area).
Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).
Cf. A019879, A019918, A019968.

Mathematica
```
First[RealDigits[Cot[Pi/9]/2, 10, 100]]
```

 5/tan(Pi/9) \\ Charles R Greathouse IV, Feb 05 2025

Equals cot(Pi/9)/2 = A019968/2.
Equals 1/(2*tan(Pi/9)) = 1/(2*A019918).
Equals A375151*cos(Pi/9) = A375151*A019879.
Equals A375151 - A375153.
Largest of the 6 real-valued roots of 192*x^6 -432*x^4 +132*x^2 -1=0. - R. J. Mathar, Aug 29 2025

A019849 Decimal expansion of sine of 40 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

This sequence is also the decimal expansion of cosine of 50 degrees. - Mohammad K. Azarian, Jun 29 2013

A sextic number with denominator 2. - Charles R Greathouse IV, Nov 05 2017

			0.642787609...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 6.

RealDigits[ Sin[ 2Pi/9], 10, 111][[1]] (* Robert G. Wilson v, Feb 16 2011 *)
RealDigits[Sin[40 Degree],10,120][[1]] (* Harvey P. Dale, Mar 27 2015 *)

sin(2/9*Pi) \\ Charles R Greathouse IV, Nov 05 2017

polrootsreal(64*x^6-96*x^4+36*x^2-3)[5] \\ Charles R Greathouse IV, Feb 05 2025

Equals cos(5*Pi/18) = 2F1(11/12,1/12;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
Equals 2*A019829*A019879. - R. J. Mathar, Jan 17 2021
A root of 64*x^6 - 96*x^4 + 36*x^2 - 3. - R. J. Mathar, Aug 29 2025

A019918 Decimal expansion of tangent of 20 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Also the decimal expansion of cotangent of 70 degrees. - Mohammad K. Azarian, Jun 30 2013

			0.36397023426620236135104788277683404389047...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 6.

Cf. A019938 (tan(2*Pi/9)).

evalf(tan(Pi/9), 100); # Bernard Schott, Apr 19 2022

First[RealDigits[Tan[Pi/9], 10, 100]] (* Paolo Xausa, Aug 01 2024 *)

tan(Pi/9) \\ Charles R Greathouse IV, Feb 05 2025

polrootsreal(x^6-33*x^4+27*x^2-3)[4] \\ Charles R Greathouse IV, Feb 05 2025

Equals tan(Pi/9) = A019829/A019879. - Bernard Schott, Apr 19 2022

Smallest positive of the 6 real roots of x^6-33*x^4+27*x^2-3=0. (Other A019978, A019938). - R. J. Mathar, Aug 31 2025

A019968 Decimal expansion of tangent of 70 degrees.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Also the decimal expansion of cotangent of 20 degrees. - Ivan Panchenko, Sep 01 2014

An algebraic number of degree 6 and denominator 3. - Charles R Greathouse IV, Aug 27 2017

			2.7474774194546222787616640264976727177518725991708258215...

Ivan Panchenko, Table of n, a(n) for n = 1..1000
Index entries for algebraic numbers, degree 6

Cf. A019879 (sine of 70 degrees).

SetDefaultRealField(RealField(100)); R:= RealField(); Tan(7*Pi(R)/18); // G. C. Greubel, Nov 21 2018

RealDigits[Tan[7*Pi/18], 10, 100][[1]] (* G. C. Greubel, Nov 21 2018 *)

tan(7*Pi/18) \\ Charles R Greathouse IV, Aug 27 2017

numerical_approx(tan(7*pi/18), digits=100) # G. C. Greubel, Nov 21 2018

Equals A019879/A019829. - R. J. Mathar, Aug 29 2025

Largest positive of the 6 real-values roots of 3*x^6 -27*x^4 +33*x^2 -1 =0. (Others: A019948, A019908). - R. J. Mathar, Aug 29 2025

A375151 Decimal expansion of the circumradius of a regular 9-gon with unit side length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 01 2024

			1.46190220008154362611637720668314585193675283...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Regular polygon.
Index entries for algebraic numbers, degree 6.

Cf. A375152 (apothem), A375153 (sagitta), A256853 (area).
Cf. circumradius of other polygons with unit side length: A020760 (triangle), A010503 (square), A300074 (pentagon), A374957 (heptagon), A285871 (octagon), A001622 (10-gon), A375190 (11-gon), A188887 (12-gon)
Cf. A019879, A121602, A272488.

Mathematica
```
First[RealDigits[Csc[Pi/9]/2, 10, 100]]
```

 5/sin(Pi/9) \\ Charles R Greathouse IV, Feb 05 2025

Equals csc(Pi/9)/2 = A121602/2.
Equals 1/(2*sin(Pi/9)) = 1/A272488.
Equals A375152/cos(Pi/9) = A375152/A019879.
Equals A375152 + A375153.
Largest of the 6 real-valued roots of 3*x^6-9*x^4+6*x^2-1=0. - R. J. Mathar, Aug 29 2025

cp's OEIS Frontend

A019819 Decimal expansion of sine of 10 degrees.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A144981 Decimal expansion of cos(Pi/8) = cos(22.5 degrees).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

SageMath

Formula

A019829 Decimal expansion of sine of 20 degrees.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A332437 Decimal expansion of 2*cos(Pi/9).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A332438 Decimal expansion of (2*cos(Pi/9))^2 = A332437^2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A019849 Decimal expansion of sine of 40 degrees.

Views

Author

Keywords