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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Area of the unit cycloid with cusp at the origin.

The arc length Integral_{theta=0..2*Pi} sqrt(2(1-cos(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

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.

FORMULA

The formula for the cycloid parameterically is x = a - sin(a) and y = 1 - cos(a).

EXAMPLE

9.424777960769379715387930149838508652591508198125317462924833776...

MATHEMATICA

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

CROSSREFS

Cf. A000796, A019692, A019694, A019669.

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

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Last modified December 12 23:32 EST 2018. Contains 318081 sequences. (Running on oeis4.)