A178817 Decimal expansion of the area of the regular 7-gon (heptagon) of edge length 1.

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

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Wikipedia, Heptagon

Wikipedia, Regular polygon

Index entries for algebraic numbers, degree 6

Formula

Equals (7/4) * cot(Pi/7).

From Michal Paulovic, Dec 27 2022: (Start)

Equals 7 / (4 * tan(Pi/7)) = 7 / (4 * A343058).

Equals sqrt(7/3 * (35 + 2 * 196^(1/3) * ((13 - 3 * sqrt(3) * i)^(1/3) + (13 + 3 * sqrt(3) * i)^(1/3)))) / 4.

Equals sqrt(7/4) * sqrt(35/12 + (637/54 - sqrt(-2401/108))^(1/3) + (637/54 + sqrt(-2401/108))^(1/3)).

(End)

A root of the polynomial 4096*x^6 - 62720*x^4 + 115248*x^2 - 16807. - Joerg Arndt, Jan 02 2023

Example

3.63391244400158899253619300760022057873501036159544491714598040951029...

Maple

evalf[120]((7/4)*cot(Pi/7)); # Muniru A Asiru, Jan 22 2019

Mathematica

RealDigits[7*Cot[Pi/7]/4, 10, 100][[1]]

Prog

(PARI) p=7; a=(p/4)*cotan(Pi/p)  \\ Set realprecision in excess. - Stanislav Sykora, Apr 12 2015
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 7*Cot(Pi(R)/7)/4; // G. C. Greubel, Jan 22 2019
(Sage) numerical_approx(7*cot(pi/7)/4, digits=100) # G. C. Greubel, Jan 22 2019

Crossrefs

Cf. A178818, A343058.

Cf. Areas of other regular polygons: A120011, A102771, A104956, A090488, A256853, A178816, A256854, A178809.

Sequence in context: A349237 A123060 A204931 * A275363 A155503 A010619

Adjacent sequences: A178814 A178815 A178816 * A178818 A178819 A178820

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jun 16 2010

Status

approved