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Decimal expansion of 4 - Pi.
6

%I #46 Mar 23 2024 13:34:31

%S 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,

%T 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,

%U 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

%N Decimal expansion of 4 - Pi.

%C 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

%C Area between a circle of radius 1 and the circumscribed square. - _Omar E. Pol_, Aug 02 2012

%C Perimeter of the unit square minus the circumference of its incircle. - _Jonathan Sondow_, Nov 23 2017

%H G. C. Greubel, <a href="/A153799/b153799.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F 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

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

%F Equals Integral_{x=0..4} sqrt(x)/(4+x) dx. - _Andy Nicol_, Mar 23 2024

%e 0.8584073464102067615373566167204971158...

%t RealDigits[4 - Pi, 10, 100][[1]] (* _Alonso del Arte_, Aug 01 2012 *)

%o (PARI) 4-Pi

%Y Essentially the same as A030644.

%Y Cf. A000796, A063448.

%K easy,nonn,cons

%O 0,1

%A _Omar E. Pol_, Jan 25 2009