A103714 Decimal expansion of the area of the surface generated by revolving one arch of the cosine curve about the x-axis.

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

Author

Sylvester Reese and Jonathan Sondow, Feb 21 2005

Keywords

• cons
• easy
• nonn

Comments

Equal to Pi times twice its analog for the parabola (see A103710).

Examples

			14.423599448414093929375465539601335358054115235952...
		

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, Pohle Colloquium Video Lecture: The universal parabolic constant, February 2005.
• Sylvester Reese and Jonathan Sondow, MathWorld: Universal Parabolic Constant.
• Wikipedia, Universal parabolic constant.

Crossrefs

Cf. 2*A000796*A103710. See also A103713.

Programs

Mathematica

RealDigits[2*Pi*(Sqrt[2] + Log[1 + Sqrt[2]]), 10, 120][[1]] (* Amiram Eldar, May 31 2023 *)

Formula

2*Pi*(sqrt(2) + log(1 + sqrt(2))).