A134030 Area of regular n-sided polygon with length of each side equal to 1 (rounded).

0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 18, 20, 23, 26, 28, 32, 35, 38, 42, 46, 49, 54, 58, 62, 67, 71, 76, 81, 86, 92, 97, 103, 109, 115, 121, 127, 134, 140, 147, 154, 161, 168, 176, 183, 191, 199, 207, 215, 223, 232, 240, 249, 258, 267, 277, 286

Offset

3,3

Links

Felix Huber, Table of n, a(n) for n = 3..10000

Kival Ngaokrajang, Illustration of initial terms.

Wikipedia, Regular polygon.

Formula

a(n) = round(n/(4*tan(Pi/n)).

Example

The exact values of the areas of regular n-gons with side 1 for n = 3 .. 12 are:
 (1/4)*3^(1/2), 1, (5/4)*cot((1/5)*Pi), (3/2)*3^(1/2), (7/4)*cot((1/7)*Pi), 2*cot((1/8)*Pi), (9/4)*cot((1/9)*Pi), (5/2)*cot((1/10)*Pi), (11/4)*cot((1/11)*Pi), 3*cot((1/12)*Pi).
The floating-point values are [0.4330127020, 1, 1.720477400, 2.598076212, 3.633912443, 4.828427124, 6.181824193, 7.694208842, 9.365639904, 11.19615242], so the rounded values are [0, 1, 2, 3, 4, 5, 6, 8, 9, 11]. - N. J. A. Sloane, Mar 11 2024

Prog

(PARI) a(n) = round(n / (4*tan(Pi/n))); \\ Michel Marcus, Sep 04 2013

Crossrefs

Cf. A064313 (same with floor).

Sequence in context: A050418 A011869 A177738 * A226189 A235592 A100054

Adjacent sequences: A134027 A134028 A134029 * A134031 A134032 A134033

Keyword

easy,nonn

Author

Ben Paul Thurston, Jan 11 2008

Extensions

Corrected by N. J. A. Sloane, Mar 11 2024 at the suggestion of Felix Huber

Status

approved