A153799 Decimal expansion of 4 - Pi.

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

Offset: 0

Author

Omar E. Pol, Jan 25 2009

Keywords

• easy
• nonn
• cons

Comments

Given a square with a side measuring 2 units, having a circle with a radius of 2 units centered on one of its corners, and another circle also with a radius of 2 units centered on the most distant corner from the one on which the first circle is centered, there are two "zones" within the square that overlap with the area of only one of the circles. This number gives the area of either zone. - Alonso del Arte, Aug 01 2012

Area between a circle of radius 1 and the circumscribed square. - Omar E. Pol, Aug 02 2012

Perimeter of the unit square minus the circumference of its incircle. - Jonathan Sondow, Nov 23 2017

Examples

			0.8584073464102067615373566167204971158...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000
• Index entries for transcendental numbers

Crossrefs

Essentially the same as A030644.

Cf. A000796, A063448.

Programs

Mathematica

RealDigits[4 - Pi, 10, 100][[1]] (* Alonso del Arte, Aug 01 2012 *)

PARI

4-Pi

Formula

4 - Pi = (-1)(Pi - 4) = (-1)*Sum_{n >= 1} (4*(-1)^n/(2*n + 1)) = (-1)*arcsin(sin 4). - Alonso del Arte, Aug 01 2012

Equals Integral_{x=0..Pi} cos(x)^2/(1 + sin(x))^2 dx. - Amiram Eldar, Aug 21 2020

Equals Integral_{x=0..4} sqrt(x)/(4+x) dx. - Andy Nicol, Mar 23 2024