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%I #45 Sep 20 2020 03:44:15
%S 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,
%T 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,
%U 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
%N Decimal expansion of 1/(2*Pi).
%C 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
%C Radius of circle having circumference 1. - _Clark Kimberling_, Jan 06 2014
%C 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
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html#section9.6">9.6 Pythagorean Triples and Pi</a>, 2019.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlouffesConstants.html">Plouffe's Constants</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 0.15915494309189533576888376337251...
%t RealDigits[N[1/(2 Pi), 100]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 18 2009 *)
%o (PARI) 1/(2*Pi) \\ _Michel Marcus_, Mar 28 2020
%Y Cf. A000796 (Pi), A019692 (2*Pi).
%K nonn,cons
%O 0,2
%A _Eric W. Weisstein_, Jul 12 2003
%E Link corrected by _Fred Daniel Kline_, Jul 29 2015
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