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

0,2

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

References

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

Links

Table of n, a(n) for n=0..101.

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.

Example

0.15915494309189533576888376337251...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A127414 A186192 A231532 * A362742 A010490 A021173

Adjacent sequences: A086198 A086199 A086200 * A086202 A086203 A086204

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 12 2003

Extensions

Link corrected by Fred Daniel Kline, Jul 29 2015

Status

approved