A329912 -id:A329912 - cp's OEIS frontend

A160510 Decimal expansion of exp(Pi/4).

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

Offset: 1

Hagen von Eitzen, May 16 2009

Identified by Knuth as one of those "quantities that are frequently used in standard subroutines and in analysis of computer programs." - Alonso del Arte, Feb 03 2012

			Exp(Pi/4) = 2.1932800507380154565597696592787382234616+ according to Knuth, appendix B, table 1.

D. E. Knuth, The Art Of Computer Programming, Vol 1: Fundamental Algorithms, Addison-Wesley, 1968.

Greg Egan, Puzzle in which this value arises naturally
Grant Sanderson and Brady Haran, Darts in Higher Dimensions, Numberphile video (2019)

Cf. A000796, A320428 (continued fraction), A329912 (Engel expansion).

evalf(exp(Pi/4), 125);  # Alois P. Heinz, Nov 17 2019

RealDigits[ E^(Pi/4), 10, 111][[1]] (* Robert G. Wilson v, May 29 2009 *)

exp(Pi/4) \\ Charles R Greathouse IV, Jan 04 2016

More terms from Robert G. Wilson v, May 29 2009

A320428 Continued fraction expansion of exp(Pi/4).

Original entry on oeis.org

2, 5, 5, 1, 3, 25, 1, 1, 17, 1, 3, 3, 1, 12, 1, 8, 5, 3, 1, 46, 3, 4, 12, 1, 5, 22, 3, 2, 1, 7, 4, 2, 1, 13, 13, 8, 1, 1, 3, 1, 1, 1, 2, 1, 11, 1, 5, 2, 1, 4, 7, 1, 71, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 4, 6, 1, 9, 1, 1, 1, 6, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 2, 1, 1, 5, 2, 1, 2, 10, 1, 19, 2, 2, 4, 1

Offset: 0

Grant T Sanderson, Aug 28 2019

This value arises naturally by taking the ratio of the volume of a unit 2n-dimensional ball to the volume of the 2n-dimensional cube containing it (with side length 2) and summing over all n.

Greg Egan, Puzzle in which this value arises naturally
Grant Sanderson and Brady Haran, Darts in Higher Dimensions, Numberphile video (2019)

Cf. A160510 (decimal expansion), A058287, A087299, A329912 (Engel expansion).

Mathematica
```
ContinuedFraction[Exp[Pi/4], 100]
```

contfrac(exp(Pi/4)) \\ Felix Fröhlich, Aug 28 2019

cp's OEIS Frontend

A160510 Decimal expansion of exp(Pi/4).

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