

A197723


Decimal expansion of (3/2)*Pi.


13



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

1,1


COMMENTS

As radians, this is equal to 270 degrees or 300 gradians.
Multiplying a number by i (with i being the imaginary unit sqrt(1)) is equivalent to rotating it by this number of radians on the complex plane.
Named 'Pau' by Randall Munroe, as a humorous compromise between Pi and Tau.  Orson R. L. Peters, Jan 08 2017
(3*Pi/2)*a^2 is the area of the cardioid whose polar equation is r = a*(1+cos(t)) and whose Cartesian equation is (x^2+y^2a*x)^2 = a^2*(x^2+y^2). The length of this cardioid is 8*a. See the curve at the Mathcurve link.  Bernard Schott, Jan 29 2020


LINKS

Eric Weisstein's World of Mathematics, Cardioid


FORMULA

2*Pi  Pi/2 = Pi + Pi/2.
Equals Integral_{t=0..Pi} (1+cos(t))^2 dt.  Bernard Schott, Jan 29 2020
Equals 4 + Sum_{k>=1} (k+1)*2^k/binomial(2*k,k).  Amiram Eldar, Aug 19 2020


EXAMPLE

4.712388980384689857693965074919254326296...


MAPLE



MATHEMATICA

RealDigits[3Pi/2, 10, 105][[1]]


PROG



CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



