A086201 Decimal expansion of 1/(2*Pi).

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

Offset: 0

Author

Eric W. Weisstein, Jul 12 2003

Keywords

• nonn
• cons

Comments

If a single hump of cycloid, with arc length 8*radius (generating circle), is inside a rectangle with width=2*radius and length=2*Pi*radius, then the radius must be 1/(2*Pi) (this sequence) to have (2/Pi), A060294, as semi arc of cycloid (arc = 4/Pi = A088538) and the rectangle... length = 1, width = 1/Pi. I suppose that in 3D geometry, gliding along a cycloid, in all directions around, from a point A at the height of 1/Pi, gives Pi*point B. - Eric Desbiaux, Dec 21 2008

Radius of circle having circumference 1. - Clark Kimberling, Jan 06 2014

The number of primitive Pythagorean triangles with hypotenuse less than N is approximately N/(2*Pi), found by Lehmer, cf. Knott link. - Frank Ellermann, Mar 27 2020

Examples

			0.15915494309189533576888376337251...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4, p. 493.

Links

• Ron Knott, 9.6 Pythagorean Triples and Pi, 2019.
• Eric Weisstein's World of Mathematics, Plouffe's Constants.
• Eric Weisstein's World of Mathematics, Pythagorean Triple.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000796 (Pi), A019692 (2*Pi).

Programs

Mathematica

RealDigits[N[1/(2 Pi), 100]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

PARI

1/(2*Pi) \\ Michel Marcus, Mar 28 2020

Extensions

Link corrected by Fred Daniel Kline, Jul 29 2015