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 1-6 of 6 results.

A236556 Decimal expansion of the steradian solid angle subtended by one square facet of the cuboctahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Jan 28 2014

Keywords

Comments

Also the vertex solid angle of a regular octahedron.

Examples

			1.35934763781648774838557005356705626555297876132983228572769584995966...

Links

Crossrefs

Cf. A188615, A236555. Icosidodecahedron: A319881, A319883. Vertex Angles: A019669, A236557, A236558.

Programs

  • Maple
    evalf(4*arcsin(1/3),100) ; # R. J. Mathar, Apr 26 2021
  • Mathematica
    RealDigits[4*ArcSin[1/3], 10, 120][[1]] (* Amiram Eldar, May 22 2023 *)
  • PARI
    4*asin(1/3)

Formula

Equals 4*arcsin(1/3) = 4*A188615.
Equals 2*Pi - 4*arcsin(2*sqrt(2)/3). - Bradley Klee, Oct 04 2018
8*A236555 + 6*this = 4*Pi. - Bradley Klee, Oct 04 2018

Extensions

Definition corrected by Bradley Klee, Oct 04 2018

A236557 Vertex solid angle (steradians) in a regular icosahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Jan 28 2014

Keywords

Examples

			2.6345470260447546596513034674924022914118092285116431884051417273...

Links

Crossrefs

Cf. Analogs: A236555 (tetrahedron), A236556 (octahedron), A019669 (cube), A236558 (dodecahedron).

Programs

  • Mathematica
    RealDigits[2*Pi - 5*ArcSin[2/3], 10, 120][[1]] (* Amiram Eldar, May 22 2023 *)
  • PARI
    2*Pi-5*asin(2/3)

Formula

Equals 2*Pi - 5*arcsin(2/3).

A236558 Vertex solid angle (steradians) in a regular dodecahedron.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Jan 28 2014

Keywords

Examples

			2.9617391537973149678740903860233946481841958625459137019202715623145...

Links

Crossrefs

Cf. Analogs: A236555 (tetrahedron), A236556 (octahedron), A019669 (cube), A236557 (icosahedron).

Programs

  • Mathematica
    RealDigits[Pi - ArcTan[2/11], 10, 120][[1]] (* Amiram Eldar, May 22 2023 *)
  • PARI
    Pi-atan(2/11)

Formula

Equals Pi - arctan(2/11).

A363437 Decimal expansion of the volume of the regular tetrahedron inscribed in the unit-radius sphere.

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Jun 02 2023

Keywords

Examples

			0.51320023927966734623035447155729551613120155668455...

Links

Crossrefs

Cf. A118273 (cube), A122553 (regular octahedron), A339259 (regular icosahedron), A363438 (regular dodecahedron).
Other constants related to the regular tetrahedron: A020781, A020829, A137914, A156546, A187110, A210974, A232812, A236555.

Programs

Formula

Equals 8/(9*sqrt(3)).
Equals A118273 / 3.
Equals A020829 / A187110 ^ 3.

A319881 Decimal expansion of the steradian solid angle subtended by one triangular facet of the icosidodecahedron.

Original entry on oeis.org

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

Views

Author

Bradley Klee, Sep 30 2018

Keywords

Examples

			0.17985349979247827058855299725610823601297353682919...

Links

Crossrefs

Cf. A319883. Cuboctahedron: A236555, A236556.

Programs

  • Mathematica
    RealDigits[3*ArcTan[2] - Pi, 10, 80][[1]]
  • PARI
    3*atan(2)-Pi \\ Altug Alkan, Oct 03 2018

Formula

Equals 3*arctan(2) - Pi.
Equals (Pi - 3*A319883)/5.

A319883 Decimal expansion of the steradian solid angle subtended by one pentagonal facet of the icosidodecahedron.

Original entry on oeis.org

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

Views

Author

Bradley Klee, Sep 30 2018

Keywords

Examples

			0.74744171820913396183995946566632056804410057174304...

Links

Crossrefs

Cf. A319881. Cuboctahedron: A236555, A236556.

Programs

  • Mathematica
    RealDigits[2*Pi - 5*ArcTan[2], 10, 80][[1]]

Formula

Equals 2*Pi - 5*arctan(2).
Equals (Pi - 5*A319881)/3.
Showing 1-6 of 6 results.

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