A197723 - OEIS

%I #58 Jan 16 2023 11:18:04

%S 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,

%T 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,

%U 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

%N Decimal expansion of (3/2)*Pi.

%C As radians, this is equal to 270 degrees or 300 gradians.

%C 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.

%C Named 'Pau' by Randall Munroe, as a humorous compromise between Pi and Tau. - _Orson R. L. Peters_, Jan 08 2017

%C (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^2-a*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

%H Ivan Panchenko, <a href="/A197723/b197723.txt">Table of n, a(n) for n = 1..1000</a>

%H Robert Ferréol, <a href="https://www.mathcurve.com/courbes2d.gb/cardioid/cardioid.shtml">Cardioid</a>, Mathcurve.

%H Randall Munroe, <a href="http://xkcd.com/1292/">xkcd: Pi vs. Tau</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cardioid.html">Cardioid</a>

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

%F 2*Pi - Pi/2 = Pi + Pi/2.

%F Equals Integral_{t=0..Pi} (1+cos(t))^2 dt. - _Bernard Schott_, Jan 29 2020

%F Equals -4 + Sum_{k>=1} (k+1)*2^k/binomial(2*k,k). - _Amiram Eldar_, Aug 19 2020

%e 4.712388980384689857693965074919254326296...

%p Digits:=100: evalf(3*Pi/2); # _Wesley Ivan Hurt_, Jan 08 2017

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

%o (PARI) 3*Pi/2 \\ _Charles R Greathouse IV_, Jul 06 2018

%Y Cf. A019669, A003881, A347152.

%K nonn,cons

%O 1,1

%A _Alonso del Arte_, Oct 17 2011