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 1-5 of 5 results.

A384474 Decimal expansion of the middle interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, May 30 2025

Keywords

Examples

			1.891345594448510418687173478952739199024779225...

References

  • Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.
  • Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 181-182.

Links

Crossrefs

Cf. A228719, A384473 (in degrees).
Cf. A002194, A019824, A177870.
Cf. A384475, A384476, A384477, A384478.

Programs

  • Mathematica
    RealDigits[3Pi/4-ArcSin[Sqrt[3]Sin[Pi/12]],10,100][[1]] (* or *)
RealDigits[Pi+ArcTan[(3-Sqrt[3]+Sqrt[6Sqrt[3]-4])/(3-Sqrt[3]-Sqrt[6Sqrt[3]-4])],10,100][[1]]

Formula

Equals 3*Pi/4 - arcsin(sqrt(3)*sin(Pi/12)).
Equals Pi + arctan((3 - sqrt(3) + sqrt(6*sqrt(3) - 4))/(3 - sqrt(3) - sqrt(6*sqrt(3) - 4))).
Equals (3*Pi - 2*A384476 - A384478)/2.
A384476 < this constant < A384478.

A384475 Decimal expansion of the smallest interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, May 30 2025

Keywords

Examples

			107.03782592159414945517598606453616977939418394...

References

  • Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.

Links

Crossrefs

Cf. A228719, A384476 (in radians).
Cf. A384474, A384476, A384477, A384478.

Programs

  • Mathematica
    RealDigits[180(1 + ArcTan[(-10 + 10 Sqrt[3] + 2 Sqrt[-4 + 6 Sqrt[3]] +2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] -3 Sqrt[2 (8 - 2 Sqrt[3] -Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])])/(2 + 2 Sqrt[3] + 2 Sqrt[6 (-2 + 3 Sqrt[3])] - 4 Sqrt[-4 + 6 Sqrt[3]] - 2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] - 3 Sqrt[2 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] +Sqrt[-4 + 6 Sqrt[3]])])]/Pi),10,100][[1]]

Formula

Equals (540 - 2*A384473 - A384477)/2.

A384476 Decimal expansion of the smallest interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, May 30 2025

Keywords

Examples

			1.868162486508351777580347333859167703515452195...

References

  • Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.

Links

Crossrefs

Cf. A228719, A384475 (in degrees).
Cf. A384473, A384474, A384477, A384478.

Programs

  • Mathematica
    RealDigits[Pi + ArcTan[(-10 + 10 Sqrt[3] + 2 Sqrt[-4 + 6 Sqrt[3]] +2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] -3 Sqrt[2 (8 - 2 Sqrt[3] -Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])])/(2 + 2 Sqrt[3] + 2 Sqrt[6 (-2 + 3 Sqrt[3])] - 4 Sqrt[-4 + 6 Sqrt[3]] - 2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] - 3 Sqrt[2 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] +Sqrt[-4 + 6 Sqrt[3]])])],10,100][[1]]

Formula

Equals (3*Pi - 2*A384474 - A384478)/2.

A384477 Decimal expansion of the largest interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, May 30 2025

Keywords

Examples

			109.19210783168876707355415731659880064894477011...

References

  • Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.

Links

Crossrefs

Cf. A228719, A384478 (in radians).
Cf. A384473, A384474, A384475, A384476.

Programs

  • Mathematica
    RealDigits[(90 (Pi + 4 ArcCsc[2/Sqrt[2 - Sqrt[2 (5 - 2 Sqrt[3] + Sqrt[-187 + 108 Sqrt[3]])]]]))/Pi,10,100][[1]]

Formula

Equals 540 - 2*(A384473 + A384475).
Equals (90*(Pi + 4*arccsc(2/sqrt(2 - sqrt(2*(5 - 2*sqrt(3) + sqrt(-187 + 108*sqrt(3))))))))/Pi.

A384478 Decimal expansion of the largest interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, May 30 2025

Keywords

Examples

			1.9057617988556553228528885242146948475110453569...

References

  • Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.

Links

Crossrefs

Cf. A228719, A384477 (in degrees).
Cf. A384473, A384474, A384475, A384476.

Programs

  • Mathematica
    RealDigits[((Pi + 4 ArcCsc[2/Sqrt[2 - Sqrt[2 (5 - 2 Sqrt[3] + Sqrt[-187 + 108 Sqrt[3]])]]]))/2,10,100][[1]]

Formula

Equals 3*Pi - 2*(A384474 + A384476).
Equals ((Pi + 4*arccsc(2/sqrt(2 - sqrt(2*(5 - 2*sqrt(3) + sqrt(-187 + 108*sqrt(3))))))))/2.
Showing 1-5 of 5 results.

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