

A122952


Decimal expansion of 3*Pi.


8



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, 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, 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
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OFFSET

1,1


COMMENTS

Area of the unit cycloid with cusp at the origin, whose parametric formula is x = t  sin(t) and y = 1  cos(t).
The arc length Integral_{theta=0..2*Pi} sqrt(2(1cos(theta))) (d theta) = 8.
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
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


REFERENCES

Anton, Bivens & Davis, Calculus, Early Transcendentals, 7th Edition, John Wiley & Sons, Inc., NY 2002, p. 490.
William H. Beyer, Editor, CRC St'd Math. Tables, 27th Edition, CRC Press, Inc., Boca Raton, FL, 1984, p. 214.


LINKS

Table of n, a(n) for n=1..105.
Robert FerrÃ©ol, Nephroid, Mathcurve.
Eric Weisstein's World of Mathematics, Cycloid.


EXAMPLE

9.424777960769379715387930149838508652591508198125317462924833776...


MATHEMATICA

RealDigits[3Pi, 10, 111][[1]]


CROSSREFS

Cf. A000796, A019692, A019694, A019669.
Cf. A093828, A180434, A197723.
Sequence in context: A319530 A318410 A245298 * A039663 A155535 A099879
Adjacent sequences: A122949 A122950 A122951 * A122953 A122954 A122955


KEYWORD

cons,nonn


AUTHOR

Robert G. Wilson v, Sep 30 2006


STATUS

approved



