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

Author

Omar E. Pol, Aug 02 2012

Keywords

• nonn
• cons

Comments

Decimal expansion of (4 - Pi)/4.

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

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

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

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

Examples

			0.21460183660255169038433915418012427895070765015622...
		

Links

• M. L. Glasser, A note on Beukers's and related integrals, Amer. Math. Monthly 126(4) (2019), 361-363.
• Index entries for transcendental numbers

Crossrefs

Cf. A003881, A153799.

Essentially the same as A091651.

Programs

Mathematica

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

PARI

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

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

Extensions

More terms from David Scambler, Aug 02 2012