A272535 Decimal expansion of the edge length of a regular 16-gon with unit circumradius.

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

Offset

0,1

Comments

Like all m-gons with m equal to a power of 2 (see A003401 and A000079), this is a constructible number.

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.

Formula

Equals 2*sin(Pi/m) for m=16, 2*A232738.

Equals sqrt(2-sqrt(2+sqrt(2))).

Minimal polynomial: x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 2. - Amiram Eldar, May 19 2026

Example

0.390180644032256535696569736954044481855383235503909615509004...

Mathematica

RealDigits[N[2Sin[Pi/16], 100]][[1]] (* Robert Price, May 02 2016*)

Prog

(PARI) 2*sin(Pi/16)

Crossrefs

Cf. A000079, A003401, A232738.

Edge lengths of other constructible m-gons: A002194 (m=3), A002193 (4), A182007 (5), A101464 (8), A094214 (10), A101263 (12), A272534 (15), A228787 (17), A272536 (20).

Sequence in context: A274400 A200495 A329937 * A016626 A126321 A335777

Adjacent sequences: A272532 A272533 A272534 * A272536 A272537 A272538

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 02 2016

Status

approved