A180434 Decimal expansion of constant (2 - Pi/2).

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

Offset

0,1

Comments

(2-Pi/2)*a^2 is the area of the loop of the right strophoid (also called the Newton strophoid) whose polar equation is r = a*cos(2*t)/cos(t) and whose Cartesian equation is x*(x^2+y^2) = a*(x^2-y^2) or y = +- x*sqrt((a-x)/(a+x)). See the curve with its loop at the Mathcurve link; the loop appears for -Pi/4 <= t <= Pi/4. - Bernard Schott, Jan 28 2020

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Robert Ferréol, Right strophoid, Math Curve.

Nikita Kalinin and Mikhail Shkolnikov, The number Pi and summation by SL(2,Z), arXiv:1701.07584 [math.NT], 2016. Gives a formula.

Index entries for transcendental numbers

Formula

Equals Integral_{t=0..Pi/4} ((cos(2*t))/cos(t))^2 dt. - Bernard Schott, Jan 28 2020

From Amiram Eldar, May 30 2021: (Start)

Equals Sum_{k>=1} 2^k/(binomial(2*k,k)*k*(2*k + 1)).

Equals Integral_{x=0..1} arcsin(x)*arccos(x) dx. (End)

Example

0.42920367320510338076867830836024855790141530...

Mathematica

RealDigits[2-Pi/2, 10, 120][[1]] (* Harvey P. Dale, Oct 12 2013 *)

Crossrefs

Cf. A004601, A180433, A222362.

Sequence in context: A201531 A021237 A115881 * A201574 A077809 A201281

Adjacent sequences: A180431 A180432 A180433 * A180435 A180436 A180437

Keyword

cons,easy,nonn

Author

Jonathan Vos Post, Sep 05 2010

Extensions

Corrected by Carl R. White, Sep 09 2010

More terms from N. J. A. Sloane, Sep 23 2010

Status

approved