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.

A352453 Decimal expansion of the area of intersection of 4 unit-radius circles that have the vertices of a unit-side square as centers.

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Mar 16 2022

Keywords

Comments

The solution to a problem in Jones (1932): "At each corner of a garden, surrounded by a wall n yards square, a goat is tied with a rope n yards long. Find the area of the part of the garden common to the four goats." (When the square is taken to be of unit size, the common area is this constant.)
The perimeter of the shape formed by the intersection is 2*Pi/3 (A019693).
The solution to the three-dimensional version of this problem is A352454.

Examples

			0.31514674362772045262676811958729526112291787931465...

Links

Crossrefs

Cf. A002194, A019670, A019693.
Cf. A075838, A133731, A192930, A352454.

Programs

  • Mathematica
    RealDigits[1 + Pi/3 - Sqrt[3], 10, 100][[1]]

Formula

Equals 1 + Pi/3 - sqrt(3) = 1 + A019670 - A002194.

A075838 Decimal expansion of the solution to the donkey problem.

Original entry on oeis.org

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

Views

Author

Zak Seidov, Oct 17 2002

Keywords

Examples

			0.95284786465494194744133321858048335174752156080640...

Links

Crossrefs

Cf. A133731, A173571, A192930.

Programs

  • Mathematica
    RealDigits[x /. FindRoot[4*x*Cos[x]^2 + Pi/2 - 2*x - Sin[2*x] == 0, {x, 1}, WorkingPrecision -> 120], 10, 105][[1]] (* Amiram Eldar, Apr 29 2023 *)
  • PARI
    solve(x=0, 1, 4*x*cos(x)^2 + Pi/2 - 2*x - sin(2*x)) \\ Michel Marcus, Sep 19 2017

Formula

x: 4x*cos^2(x) + (1/2)Pi - 2x - sin(2x) = 0.

A191102 Decimal expansion of (1/3)*arccos(6/Pi^2-1).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Jul 12 2011

Keywords

Examples

			.65789338396252593180869437710606678919613274849811661638...

Links

Crossrefs

Cf. A192930, A229099.

Programs

  • Mathematica
    RealDigits[(ArcCos[6/Pi^2-1])/3,10,120][[1]] (* Harvey P. Dale, Nov 29 2015 *)
  • PARI
    acos(6/Pi^2-1)/3 \\ Michel Marcus, Sep 19 2017
Showing 1-3 of 3 results.

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

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