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
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.
Programs
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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))).
Comments