A177870 Decimal expansion of 3*Pi/4.

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, 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, 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

Offset: 1

Author

R. J. Mathar, Dec 13 2010

Keywords

• nonn
• cons
• easy

Comments

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

Ratio of the area of an arbelos to the area of its associated parbelos. - Jonathan Sondow, Nov 28 2013

(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

The smallest nonnegative solution to sin(x) = -cos(x). - Wolfe Padawer, Apr 12 2023

Examples

			2.35619449019234492884698253745962716314787704953132936573120...
		

References

• Jonathan Borwein & Peter Borwein, A Dictionary of Real Numbers. Pacific Grove, California: Wadsworth & Brooks/Cole Advanced Books & Software (1990) p. 168

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Robert Ferréol, Cissoid of Diocles, Mathcurve.
• Jonathan Sondow, The parbelos, a parabolic analog of the arbelos, arXiv:1210.2279 [math.HO], 2012-2013: Amer. Math. Monthly 120 (2013) 929-935.
• E. Tsukerman, Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos, arXiv:1210.5580 [math.MG], 2012-2013.
• Index to sequences related to curves
• Index entries for transcendental numbers

Crossrefs

Reciprocal of A232715.

Cf. A000796, A003881, A019675, A122952.

Programs

Maple

evalf(3*Pi/4) ;

Mathematica

RealDigits[N[3(Pi/4), 110]][[1]]

PARI

3*Pi/4 \\ Charles R Greathouse IV, Sep 30 2022

Formula

Equals (3/4)*A000796 = 3*A003881 = 6*A019675 = A122952/4.

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

Equals 2 * Integral_{x=0..1} x * sqrt(x/(1-x)) dx (cissoid). - Bernard Schott, Jul 14 2020

Equals Sum_{k>=1} arctan(2/k^2). - Amiram Eldar, Aug 10 2020

Equals Integral_{x=-oo..oo} (x^2 + 1)/(x^4 + 4) dx. - Kritsada Moomuang, Jun 04 2025