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A103714
Decimal expansion of the area of the surface generated by revolving one arch of the cosine curve about the x-axis.
1
1, 4, 4, 2, 3, 5, 9, 9, 4, 4, 8, 4, 1, 4, 0, 9, 3, 9, 2, 9, 3, 7, 5, 4, 6, 5, 5, 3, 9, 6, 0, 1, 3, 3, 5, 3, 5, 8, 0, 5, 4, 1, 1, 5, 2, 3, 5, 9, 5, 2, 1, 0, 0, 1, 2, 9, 2, 1, 7, 6, 5, 3, 4, 9, 2, 2, 6, 2, 6, 0, 7, 2, 9, 7, 2, 2, 1, 9, 5, 3, 9, 3, 0, 2, 9, 2, 4, 3, 8, 4, 2, 1, 9, 5, 5, 3, 9, 6, 5, 8, 6, 5, 9, 8, 6
OFFSET
2,2
COMMENTS
Equal to Pi times twice its analog for the parabola (see A103710).
REFERENCES
Clyde E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, p. 288.
Sylvester Reese, A universal parabolic constant, 2004, preprint.
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2022, sec. 8.1.
Sylvester Reese and Jonathan Sondow, MathWorld: Universal Parabolic Constant.
FORMULA
2*Pi*(sqrt(2) + log(1 + sqrt(2))).
EXAMPLE
14.423599448414093929375465539601335358054115235952...
MATHEMATICA
RealDigits[2*Pi*(Sqrt[2] + Log[1 + Sqrt[2]]), 10, 120][[1]] (* Amiram Eldar, May 31 2023 *)
CROSSREFS
Cf. 2*A000796*A103710. See also A103713.
Sequence in context: A068923 A222295 A371706 * A260486 A193514 A112108
KEYWORD
cons,easy,nonn
AUTHOR
Sylvester Reese and Jonathan Sondow, Feb 21 2005
STATUS
approved