

A177870


Decimal expansion of 3*Pi/4.


3



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
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OFFSET

1,1


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/(ax)). See the curve at the Mathcurve link and formula.  Bernard Schott, Jul 14 2020


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 FerrÃ©ol, Cissoid of Diocles, Mathcurve.
J. Sondow, The parbelos, a parabolic analog of the arbelos, arXiv:1210.2279 [math.HO], 20122013: Amer. Math. Monthly 120 (2013) 929935.
E. Tsukerman, Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos, arXiv 2012.
Index to sequences related to curves.


FORMULA

Equals 0.75*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/(1x)) dx (cissoid).  Bernard Schott, Jul 14 2020
Equals Sum_{k>=1} arctan(2/k^2).  Amiram Eldar, Aug 10 2020


EXAMPLE

2.35619449019234492884698253745962716314787704953132936573120...


MAPLE

evalf(3*Pi/4) ;


MATHEMATICA

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


CROSSREFS

Reciprocal of A232715.
Cf. A000796, A003881, A019675, A122952.
Sequence in context: A157260 A336017 A291486 * A094872 A201744 A152206
Adjacent sequences: A177867 A177868 A177869 * A177871 A177872 A177873


KEYWORD

nonn,cons,easy


AUTHOR

R. J. Mathar, Dec 13 2010


STATUS

approved



