cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A064313 Integer part of area of a regular polygon with n sides each of length 1.

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 4, 6, 7, 9, 11, 13, 15, 17, 20, 22, 25, 28, 31, 34, 38, 41, 45, 49, 53, 57, 62, 66, 71, 76, 81, 86, 91, 97, 102, 108, 114, 120, 127, 133, 140, 146, 153, 160, 168, 175, 183, 190, 198, 206, 214, 223, 231, 240, 249, 258, 267, 276, 286, 295, 305, 315
Offset: 2

Views

Author

Henry Bottomley, Oct 15 2001

Keywords

Comments

Usually (perhaps always?) floor(n^2/(4*Pi) - Pi/12) for a polygon of circumference n. Note that the area of a circle with circumference C is C^2/(4*Pi).

Examples

			Areas (starting from n=2) are: 0, 0.433... (equilateral triangle), 1 (square), 1.720... (pentagon), 2.598... (hexagon), 3.633... (heptagon), 4.828... (octagon), etc., so sequence starts 0, 0, 1, 1, 2, 3, 4, etc.

Links

Crossrefs

Cf. A134030.

Programs

  • Maple
    A064313 := proc(n) RETURN(floor((n/4)*cot(Pi/n))) end:
  • Mathematica
    Table[ Floor[(n/4)*Cot[Pi/n]], {n, 2, 75} ]
  • PARI
    { for (n=2, 1000, if (n>2, a=n\(4*tan(Pi/n)), a=0); write("b064313.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 11 2009

Formula

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

A343946 Surface area of a right prism whose base is a regular n-gon with unit side length and unit height (rounded to the nearest integer).

Original entry on oeis.org

4, 6, 8, 11, 14, 18, 21, 25, 30, 34, 39, 45, 50, 56, 62, 69, 76, 83, 91, 99, 107, 115, 124, 133, 142, 152, 162, 173, 183, 194, 206, 217, 229, 242, 254, 267, 281, 294, 308, 322, 337, 352, 367, 382, 398, 414, 431, 447, 464, 482, 500, 518, 536, 555, 574, 593, 612, 632, 653
Offset: 3

Views

Author

Wesley Ivan Hurt, May 04 2021

Keywords

Examples

			a(3) = 4; the surface area of a right prism whose base is an equilateral triangle with unit side lengths and height is 3+sqrt(3)/2 = 3.8660..., which rounds up to 4.
a(4) = 6 (surface area of a cube with unit side length and height).

Links

Crossrefs

Cf. A134030 (volume).

Programs

  • Mathematica
    Table[Round[n + n*Cot[Pi/n]/2], {n, 3, 100}]

Formula

a(n) = round(n+n*cot(Pi/n)/2).

A343947 Surface area to volume ratio of a right prism with unit height and whose base is a regular n-gon with side length 1 (rounded to the nearest integer).

Original entry on oeis.org

9, 6, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 3

Views

Author

Wesley Ivan Hurt, May 04 2021

Keywords

Crossrefs

Cf. A064313, A134030, A343946.

Programs

  • Mathematica
    Table[Round[(4 + 2 Cot[Pi/n])/Cot[Pi/n]], {n, 3, 100}]

Formula

a(n) = round((4 + 2*cot(Pi/n))/cot(Pi/n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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