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

Author

Vladimir Joseph Stephan Orlovsky, Jun 16 2010

Keywords

• nonn
• cons
• easy

Examples

			3.63391244400158899253619300760022057873501036159544491714598040951029...
		

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

Crossrefs

Cf. A178818, A343058.

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

Programs

Magma

SetDefaultRealField(RealField(100)); R:=RealField(); 7*Cot(Pi(R)/7)/4; // G. C. Greubel, Jan 22 2019

Maple

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

Mathematica

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

PARI

p=7; a=(p/4)*cotan(Pi/p)  \\ Set realprecision in excess. - Stanislav Sykora, Apr 12 2015

Sage

numerical_approx(7*cot(pi/7)/4, digits=100) # G. C. Greubel, Jan 22 2019

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