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.

A334843 Decimal expansion of arclength between (0,0) and (Pi/6,1/2) on y = sin x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 0.63397459621556135323627682924706381652859737309480968...

Links

Crossrefs

Cf. A333202, A332633, A334842.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Sin[x], x]^2], {x, 0, Pi/4}]
r = N[s, 200]
RealDigits[r][[1]]
  • PARI
    (3 - sqrt(3))/2 \\ Charles R Greathouse IV, Feb 11 2025

Formula

arclength = (3 - sqrt(3))/2.

A332634 Decimal expansion of arclength between (0,0) and (Pi/6,1) on y = tan x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 0.780131428280849333559981872217733063687522...

Crossrefs

Cf. A333202, A332633, A334843

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Tan[x], x]^2], {x, 0, Pi/6}]
r = N[s, 200]
RealDigits[r][[1]]

A334842 Decimal expansion of arclength between (0,0) and (Pi/3,sqrt(3)) on y = tan x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 2.056999740078724233251017930691409549645541986...

Crossrefs

Cf. A333202, A332633, A334843.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Tan[x], x]^2], {x, 0, Pi/3}]
r = N[s, 200]
RealDigits[r][[1]]

A336002 Decimal expansion of the number u such that the arclength on y = tan(x) from (0,0) to (u, tan u) is 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 06 2020

Keywords

Examples

			u = 0.6767706953243014485574475264257713407176...

Crossrefs

Cf. A332633, A336003.

Programs

  • Mathematica
    x = x /. FindRoot[(Sqrt[2] (ArcSin[Sin[x]/Sqrt[2]] +
       ArcTanh[(Sqrt[2] Sin[x])/Sqrt[3 + Cos[2 x]]]) Cos[x] Sqrt[
     1 + Sec[x]^2])/Sqrt[3 + Cos[2 x]] == 1, {x, 1},
   WorkingPrecision -> 200]
RealDigits[x][[1]]

A334845 Decimal expansion of arclength between (0,1) and (Pi/4,sqrt(2)) on y = sec x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 0.9246753483536079599958842623846196965880723284650...

Crossrefs

Cf. A333202, A332633.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Sec[x], x]^2], {x, 0, Pi/4}]
r = N[s, 200]
RealDigits[r][[1]]
Showing 1-5 of 5 results.

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