A210958 Decimal expansion of 1 - (Pi/4).

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

Offset

0,1

Comments

Decimal expansion of (4 - Pi)/4.

Area between a square and the inscribed quarter circle of radius 1.

Area between a circle of radius 1 and the circumscribed square, divided by 4.

Area between a circle of diameter 1 and the circumscribed square. - Omar E. Pol, Sep 24 2013

Volume between a cube of side length 1 and the inscribed cylinder. - Omar E. Pol, Sep 25 2013

The probability that three real numbers independently and uniformly selected at random in the range (0, 1) can be the lengths of the sides of an acute triangle (Lessard, 2017). - Amiram Eldar, Apr 22 2026

Links

Table of n, a(n) for n=0..86.

K. Dilcher and C. Vignat, Integrals involving arbitrary powers of the arcsine, with applications to infinite series, arXiv:2512.05260 (2025), Example 3.5.

M. L. Glasser, A note on Beukers's and related double integrals, Amer. Math. Monthly 126(4) (2019), 361-363.

Laurent Lessard, Sticks in the woods, Book Proofs, 2017.

Index entries for transcendental numbers.

Formula

1 - (Pi/4) = (4 - Pi)/4 = 1 - A003881 = A153799/4.

From Amiram Eldar, Jun 29 2020: (Start)

Equals Sum_{k>=0} (-1)^k/(2*k+3).

Equals Integral_{x=0..Pi/4} tan(x)^2 dx.

Equals Integral_{x=0..1} arcsin(x) dx /(1+x)^2.

Equals Integral_{x=1..oo} dx/(x^2+x^4). (End)

Equals -Integral_{x=0..1, y=0..1} arcsin(x*y)/((1+x*y)^2*log(x*y)) dx dy. (Apply Theorem 1 or Theorem 2 from Glasser (2019) to one of Amiram Eldar's integrals.) - Petros Hadjicostas, Jun 29 2020

Continued fraction 1/(3 + 3^2/(2 + 5^2/(2 + 7^2/(2 + ... )))). - Peter Bala, Feb 28 2024

Equals Sum_{k>=1} 2^k/(binomial(2*k,k)*2*k*(2*k+1)) [Dilcher] - R. J. Mathar, May 20 2026

Example

0.21460183660255169038433915418012427895070765015622...

Mathematica

RealDigits[1 - Pi/4, 10, 87][[1]] (* Bruno Berselli, Aug 03 2012 *)

Prog

(PARI) 1-Pi/4 \\ Charles R Greathouse IV, Oct 01 2022

Crossrefs

Cf. A003881, A153799.

Essentially the same as A091651.

Sequence in context: A083007 A309845 A002987 * A188925 A063872 A199909

Adjacent sequences: A210955 A210956 A210957 * A210959 A210960 A210961

Keyword

nonn,cons

Author

Omar E. Pol, Aug 02 2012

Extensions

More terms from David Scambler, Aug 02 2012

Status

approved