A272536 Decimal expansion of the edge length of a regular 20-gon with unit circumradius.

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

Offset: 0

Author

Stanislav Sykora, May 02 2016

Keywords

• nonn
• cons
• easy

Comments

Since 20-gon is constructible (see A003401), this is a constructible number.

Examples

			0.3128689300804617380202106389343337846277997841713215801692826921...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Mauro Fiorentini, Construibili (numeri)
• Eric Weisstein's World of Mathematics, Constructible Number
• Wikipedia, Constructible number
• Wikipedia, Regular polygon
• Index entries for algebraic numbers, degree 8.

Crossrefs

Cf. A003401.

Edge lengths of other constructible m-gons: A002194 (m=3), A002193 (4), A182007 (5), A101464 (8), A094214 (10), A101263 (12), A272534 (15), A272535 (16), A228787 (17).

Cf. A019818.

Programs

Mathematica

RealDigits[N[2Sin[Pi/20], 100]][[1]] (* Robert Price, May 02 2016*)

PARI

2*sin(Pi/20)

Formula

Equals 2*sin(Pi/20) = 2*A019818.

Equals also (sqrt(2)+sqrt(10)-2*sqrt(5-sqrt(5)))/4.

Equals i^(9/10) + i^(-9/10). - Gary W. Adamson, Jul 08 2022