A019699 Decimal expansion of 2*Pi/15 = (4*Pi/3)/10.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

With offset 1, decimal expansion of 4*Pi/3, the volume of a sphere of radius 1. - Omar E. Pol, Aug 27 2007, Sep 25 2013

2*Pi/15 is the common value of the base angles of the isosceles triangle formed at the common vertex of the figure obtained by gluing a hexagon and a pentagon, both regular, along a common side, as shown in the CNRS link. - Michel Marcus, Mar 06 2015

This is also the surface area (in some cubic length unit (l.u.)) of a sphere with a central cylinder symmetrical hole of length 2 l.u. Thanks to Sven Heinemeyer for reminding me of this classical astonishing result. See e.g., Bild der Wissenschaft, Januar 1964, p. 75, or the Gardner reference, Problem 7 on p. 51. In two dimensions things are different. See A258146. - Wolfdieter Lang, May 31 2015

Examples

			2*Pi/15 = 0.418879020478639098461685784437267...
4*Pi/3 = 4.18879020478639098461685784437267... - _Omar E. Pol_, Sep 25 2013
		

References

• Bild der Wissenschaft, Januar 1964.
• Martin Gardner, Mathematische Rätsel und Probleme, 3. Auflage, Friedr. Vieweg + Sohn, Braunschweig, 1975, p. 51 (in German). In English: Mathematical Puzzles and Diversions from "Scientific American", Simon and Schuster, N. Y. 1959/1961.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Ana Rechtman, Février 2015, 4ème défi, Images des Mathématiques, CNRS, 2015.
• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A019692, A019693.

Programs

Mathematica

RealDigits[(2 Pi)/15,10,120][[1]] (* Harvey P. Dale, Mar 22 2015 *)

PARI

2*Pi/15 \\ Charles R Greathouse IV, Jan 09 2018

Formula

(1/10)*volume of the unit sphere in R^3 = (1/10)*Pi^(3/2)/gamma(1+3/2). - Benoit Cloitre, Jun 19 2003