A122952 - OEIS

A122952

Decimal expansion of 3*Pi.

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(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

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 Ferréol, Nephroid, Mathcurve.

Eric Weisstein's World of Mathematics, Cycloid.

Index entries for transcendental numbers

EXAMPLE

9.424777960769379715387930149838508652591508198125317462924833776...

MATHEMATICA

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