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%I #41 Sep 28 2022 13:36:22
%S 9,4,2,4,7,7,7,9,6,0,7,6,9,3,7,9,7,1,5,3,8,7,9,3,0,1,4,9,8,3,8,5,0,8,
%T 6,5,2,5,9,1,5,0,8,1,9,8,1,2,5,3,1,7,4,6,2,9,2,4,8,3,3,7,7,6,9,2,3,4,
%U 4,9,2,1,8,8,5,8,6,2,6,9,9,5,8,8,4,1,0,4,4,7,6,0,2,6,3,5,1,2,0,3,9,4,6,4,4
%N Decimal expansion of 3*Pi.
%C Area of the unit cycloid with cusp at the origin, whose parametric formula is x = t - sin(t) and y = 1 - cos(t).
%C The arc length Integral_{theta=0..2*Pi} sqrt(2(1-cos(theta))) (d theta) = 8.
%C 3*Pi is also the surface area of a sphere whose diameter equals the square root of 3. More generally x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - _Omar E. Pol_, Dec 18 2013
%C 3*Pi is also the area of the nephroid (an epicycloid with two cusps) whose Cartesian parametrization is: x = (1/2) * (3*cos(t) - cos(3t)) and y = (1/2) * (3*sin(t) - sin(3t)). The length of this nephroid is 12. See the curve at the Mathcurve link. - _Bernard Schott_, Feb 01 2020
%D Anton, Bivens & Davis, Calculus, Early Transcendentals, 7th Edition, John Wiley & Sons, Inc., NY 2002, p. 490.
%D William H. Beyer, Editor, CRC St'd Math. Tables, 27th Edition, CRC Press, Inc., Boca Raton, FL, 1984, p. 214.
%H Robert Ferréol, <a href="https://www.mathcurve.com/courbes2d.gb/nephroid/nephroid.shtml">Nephroid</a>, Mathcurve.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cycloid.html">Cycloid</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 9.424777960769379715387930149838508652591508198125317462924833776...
%t RealDigits[3Pi, 10, 111][[1]]
%o (PARI) 3*Pi \\ _Charles R Greathouse IV_, Sep 28 2022
%Y Cf. A000796, A019692, A019694, A019669.
%Y Cf. A093828, A180434, A197723.
%K cons,nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 30 2006
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