A392464 Decimal expansion of the area of an 18-gon with unit side lengths.

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

Offset

2,1

Comments

This constant multiplied by the square of the side length of a regular 18-gon equals the area of that 18-gon.

18^2 divided by this constant equals 72 * tan(Pi/18) = 12.69554261... which is the perimeter and the area of an equable 18-gon with its side length 4 * tan(Pi/18) = 0.70530792... .

Links

Table of n, a(n) for n=2..106.

Wikipedia, Octadecagon.

Index entries for algebraic numbers, degree 6.

Formula

Equals 9 / (2 * tan(Pi/18)).

Equals 9/2 * (sqrt(3) + 4^(1/3) * ((sqrt(3) + i)^(1/3) + (sqrt(3) - i)^(1/3))).

Equals 9 * (sqrt(3/4) + i^(1/9) + 1 / i^(1/9)).

Minimal polynomial: 64*x^6 - 42768*x^4 + 708588*x^2 - 1594323. - Amiram Eldar, May 25 2026

Example

25.5207681882796928...

Maple

evalf((9 / (2 * tan(Pi/18))), 105);

Mathematica

RealDigits[9 / (2 * Tan[Pi/18]), 10, 105][[1]]

Prog

(PARI) 9 / (2 * tan(Pi/18))
(PARI) polrootsreal(64*x^6 - 42768*x^4 + 708588*x^2 - 1594323) \\ Charles R Greathouse IV, Apr 24 2026

Crossrefs

Cf. A019889 (real(i^(1/9))), A019908 (tan(Pi/18)).

Sequence in context: A145428 A086283 A153759 * A269992 A146100 A101458

Adjacent sequences: A392461 A392462 A392463 * A392465 A392466 A392467

Keyword

nonn,cons

Author

Michal Paulovic, Feb 18 2026

Status

approved