The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A137618 Decimal expansion of surface area of the solid of revolution generated by a Reuleaux triangle rotated around one of its symmetry axes. 3
 2, 9, 9, 3, 3, 1, 7, 1, 7, 3, 4, 8, 3, 1, 3, 3, 6, 0, 3, 9, 8, 0, 4, 5, 6, 4, 3, 3, 2, 6, 6, 9, 5, 5, 3, 8, 9, 9, 5, 6, 4, 3, 8, 9, 9, 6, 3, 3, 6, 6, 1, 4, 7, 6, 6, 4, 7, 8, 7, 7, 2, 7, 2, 5, 8, 7, 5, 6, 1, 7, 8, 7, 1, 7, 6, 6, 0, 1, 6, 2, 4, 9, 5, 8, 8, 8, 1, 1, 8, 4, 9, 4, 4, 4, 7, 1, 6, 7, 2, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The rotated Reuleaux triangle is not only a surface of constant width, it is the minimum area surface of revolution with constant width (Campi et al. 1996). REFERENCES St. Campi, A. Colesanti and P. Gronchi, Minimum problems for volumes of convex bodies, Partial Differential Equations and Applications - Collected Papers in Honor of Carlo Pucci, Marcel Dekker (1996), pp. 43-55. LINKS Table of n, a(n) for n=1..101. Bernd Kawohl and Christof Weber, Meissner's Mysterious Bodies, Mathematical Intelligencer, Volume 33, Number 3, 2011, pp. 94-101. SwissEduc: Teaching and Learning Mathematics, Gleichdick - Koerper konstanter Breite (in German and English) FORMULA Equals 2*Pi - Pi^2 /3. EXAMPLE 2.99331717348313360398045643326695538995643899633661... MATHEMATICA k1[x_] := Sqrt[1 - (x - Sqrt[3]/2)^2]; k2[x_] := Sqrt[1 - x^2] - 1/2; 2*Pi*Integrate[k1[x]*Sqrt[1+D[k1[x], x]^2], {x, Sqrt[3]/2-1, 0}] + 2*Pi*Integrate[k2[x]*Sqrt[1+D[k2[x], x]^2], {x, 0, Sqrt[3]/2}] RealDigits[2*Pi - Pi^2/3, 10, 120][[1]] (* Amiram Eldar, May 22 2023 *) CROSSREFS Cf. A102888, A137615, A137616, A137617. Sequence in context: A201894 A023400 A153637 * A340866 A021338 A021889 Adjacent sequences: A137615 A137616 A137617 * A137619 A137620 A137621 KEYWORD cons,easy,nonn AUTHOR Christof Weber, Feb 04 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 8 14:02 EDT 2023. Contains 363165 sequences. (Running on oeis4.)