A280533 -id:A280533 - cp's OEIS frontend

A280725 Decimal expansion of 22*sin(Pi/22).

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

Offset: 1

Rick L. Shepherd, Jan 07 2017

The ratio of the perimeter of a regular 11-gon (hendecagon) to its diameter (largest diagonal).

Also least positive root of x^5 - 11x^4 - 484x^3 + 3993x^2 + 43923x - 161051.

			3.130926442012273089763438709560132713403129944771655225197821304298120771...

Index entries for algebraic numbers, degree 5.

Cf. For other n-gons: A010466 (n=4), 10*A019827 (n=5, 10), A280533 (n=7), A280585 (n=8), A280633 (n=9), A280819 (n=12).

evalf(22*sin(Pi/22),100); # Wesley Ivan Hurt, Feb 01 2017

RealDigits[22*Sin[Pi/22], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)

PARI
```
22*sin(Pi/22)
```

A280585 Decimal expansion of 8*sin(Pi/8).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jan 05 2017

Decimal expansion of the ratio of the perimeter of a regular 8-gon (octagon) to its diameter (largest diagonal).

			3.061467458920718173827679872243190934090756499885016331470405085020368271...

Index entries for algebraic numbers, degree 4.

Cf. For other n-gons: A010466 (n=4), 10*A019827 (n=5, 10), A280533 (n=7), A280633 (n=9), A280725 (n=11), A280819 (n=12).

Cf. A182168.

evalf(8*sin(Pi/8),100); # Wesley Ivan Hurt, Feb 01 2017

RealDigits[8*Sin[Pi/8], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)

PARI
```
8*sin(Pi/8)
```

Equals 8*A182168.

A280633 Decimal expansion of 18*sin(Pi/18).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jan 06 2017

The ratio of the perimeter of a regular 9-gon (nonagon) to its diameter (largest diagonal).

Also least positive root of x^3 - 243x + 729.

			3.125667198004746279330899281847666328006762189313248970252344806377184798...

Index entries for algebraic numbers, degree 3.

Cf. For other n-gons: A010466 (n=4), 10*A019827 (n=5, 10), A280533 (n=7),A280585 (n=8), A280725(n=11), A280819 (n=12).

evalf(18*sin(Pi/18),100); # Wesley Ivan Hurt, Feb 01 2017

RealDigits[18*Sin[Pi/18],10,120][[1]] (* Harvey P. Dale, Dec 02 2018 *)

PARI
```
18*sin(Pi/18)
```

18*A019819.

A280819 Decimal expansion of 12*sin(Pi/12).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jan 08 2017

The ratio of the perimeter of a regular 12-gon (dodecagon) to its diameter (greatest diagonal).

A quartic integer: the least positive root of x^4 - 144x^2 + 1296.

			3.105828541230249148186786051488579940188826815839166165768038487780683696...

Index entries for algebraic numbers, degree 4

Cf. For other n-gons: A010466 (n=4), 10*A019827 (n=5, 10), A280533 (n=7), A280585 (n=8), A280633 (n=9), A280725 (n=11).

First@ RealDigits@ N[12 Sin[Pi/12], 120] (* Michael De Vlieger, Feb 05 2017 *)

PARI
```
12*sin(Pi/12)
```

polrootsreal(x^4-144*x^2+1296)[3] \\ Charles R Greathouse IV, Feb 05 2017

12*A019824.

A280926 Least k such that the first n digits of the decimal expansion of the ratio of the perimeter of a regular k-gon to its diameter match those of Pi.

Original entry on oeis.org

5, 7, 29, 47, 119, 699, 1407, 4911, 18971, 46803, 119951, 363209, 1276197, 3722389, 19973297, 73605289, 183273481, 390720475, 1671075265, 4541314567, 22107473795, 44810965685, 172567099183, 617945607281, 1835952288687, 3938674815741, 19847928172101

Offset: 1

Rick L. Shepherd, Jan 10 2017

By definition, the diameter of a regular k-gon is the length of its longest diagonal.

All terms are odd; see Formula section. - Jon E. Schoenfield, Mar 29 2021

			An equilateral triangle (k=3) has no diagonals, and a square (k=4) has perimeter/diameter = sqrt(8) = 2.828427..., but a regular pentagon (k=5) has perimeter/diameter = (5/2)*(sqrt(5) - 1) = 3.090169..., whose first digit (3) matches that of Pi = 3.141592..., so a(1)=5. - _Jon E. Schoenfield_, Mar 31 2021
This ratio for a regular 7-gon (heptagon) is 3.115293... (A280533), where 3.1 equals the first two digits of Pi's decimal expansion. Because the first two digits are not 3.1 for k < 7, a(2) = 7.

Cf. A000796, A280533.

a(n) = 1 + 2*floor((1/2)*(1 + sqrt((Pi^3/24)/(Pi-floor(Pi*10^(n-1))/10^(n-1))))). - Jon E. Schoenfield, Mar 28 2021

a(13)-a(27) from Jon E. Schoenfield, Mar 28 2021

cp's OEIS Frontend

A280725 Decimal expansion of 22*sin(Pi/22).

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A280585 Decimal expansion of 8*sin(Pi/8).

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A280633 Decimal expansion of 18*sin(Pi/18).

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A280819 Decimal expansion of 12*sin(Pi/12).

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A280926 Least k such that the first n digits of the decimal expansion of the ratio of the perimeter of a regular k-gon to its diameter match those of Pi.

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