A197723 Decimal expansion of (3/2)*Pi.

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

Offset: 1

Author

Alonso del Arte, Oct 17 2011

Keywords

• nonn
• cons

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^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

Examples

			4.712388980384689857693965074919254326296...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• Robert Ferréol, Cardioid, Mathcurve.
• Randall Munroe, xkcd: Pi vs. Tau
• Eric Weisstein's World of Mathematics, Cardioid
• Index entries for transcendental numbers

Crossrefs

Cf. A019669, A003881, A347152.

Programs

Maple

Digits:=100: evalf(3*Pi/2); # Wesley Ivan Hurt, Jan 08 2017

Mathematica

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

PARI

3*Pi/2 \\ Charles R Greathouse IV, Jul 06 2018

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