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.

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A355186 Decimal expansion of 2*log(sqrt(2)+1)/Pi.

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Jun 23 2022

Keywords

Comments

The average distance between the center of a unit square to a point on its perimeter uniformly chosen by a random direction from the center.
If the point is uniformly chosen at random on the perimeter, then the average is (sqrt(2) + arcsinh(1))/4 (A345653).

Examples

			0.56109985233918012713571958893523969280887242462809...

Links

  • Mark Dalthorp, Escape the Square, Mathematics Magazine, Vol. 87, No. 1 (2014), p. 68.

Crossrefs

Cf. A019669, A060294, A091648, A345653.

Programs

  • Mathematica
    RealDigits[2*ArcSinh[1]/Pi, 10, 100][[1]]

Formula

Equals arcsinh(1)/arcsin(1).
Equals A060294 * A091648 = A091648 / A019669.
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