%I #50 Apr 14 2023 08:20:37
%S 2,3,5,6,1,9,4,4,9,0,1,9,2,3,4,4,9,2,8,8,4,6,9,8,2,5,3,7,4,5,9,6,2,7,
%T 1,6,3,1,4,7,8,7,7,0,4,9,5,3,1,3,2,9,3,6,5,7,3,1,2,0,8,4,4,4,2,3,0,8,
%U 6,2,3,0,4,7,1,4,6,5,6,7,4,8,9,7,1,0,2,6,1,1,9,0,0,6,5,8,7,8,0,0,9,8,6,6,1,1
%N Decimal expansion of 3*Pi/4.
%C As radians, this is equal to 135 degrees (on an analog clock, the span of 22 minutes and 30 seconds). - _Alonso del Arte_, Feb 03 2013
%C Ratio of the area of an arbelos to the area of its associated parbelos. - _Jonathan Sondow_, Nov 28 2013
%C (3*Pi/4)*a^2 is the area between a cissoid of Diocles and its asymptote when polar equation of cissoid is r = a*sin^2(t)/cos(t) and Cartesian equation is x * (x^2+y^2) = a * y^2 or y = +-x * sqrt(x/(a-x)). See the curve at the Mathcurve link and formula. - _Bernard Schott_, Jul 14 2020
%C The smallest nonnegative solution to sin(x) = -cos(x). - _Wolfe Padawer_, Apr 12 2023
%D Jonathan Borwein & Peter Borwein, A Dictionary of Real Numbers. Pacific Grove, California: Wadsworth & Brooks/Cole Advanced Books & Software (1990) p. 168
%H Vincenzo Librandi, <a href="/A177870/b177870.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert Ferréol, <a href="https://mathcurve.com/courbes2d.gb/cissoiddroite/cissoiddroite.shtml">Cissoid of Diocles</a>, Mathcurve.
%H Jonathan Sondow, <a href="http://arxiv.org/abs/1210.2279">The parbelos, a parabolic analog of the arbelos</a>, arXiv:1210.2279 [math.HO], 2012-2013: Amer. Math. Monthly 120 (2013) 929-935.
%H E. Tsukerman, <a href="http://arxiv.org/abs/1210.5580">Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos</a>, arXiv:1210.5580 [math.MG], 2012-2013.
%H <a href="/index/Cu">Index to sequences related to curves</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals (3/4)*A000796 = 3*A003881 = 6*A019675 = A122952/4.
%F Equals 1 + (3/5) + (3*4)/(5*7) + (3*4*5)/(5*7*9) + ... = hypergeom([3,1],[5/2],1/2). - _Peter Bala_, Oct 30 2019
%F Equals 2 * Integral_{x=0..1} x * sqrt(x/(1-x)) dx (cissoid). - _Bernard Schott_, Jul 14 2020
%F Equals Sum_{k>=1} arctan(2/k^2). - _Amiram Eldar_, Aug 10 2020
%e 2.35619449019234492884698253745962716314787704953132936573120...
%p evalf(3*Pi/4) ;
%t RealDigits[N[3(Pi/4), 110]][[1]]
%o (PARI) 3*Pi/4 \\ _Charles R Greathouse IV_, Sep 30 2022
%Y Reciprocal of A232715.
%Y Cf. A000796, A003881, A019675, A122952.
%K nonn,cons,easy
%O 1,1
%A _R. J. Mathar_, Dec 13 2010