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 A137617 Decimal expansion of volume of the solid of revolution generated by a Reuleaux triangle rotated around one of its symmetry axes. 3
 4, 4, 9, 4, 6, 1, 0, 3, 5, 5, 4, 4, 9, 6, 9, 0, 5, 5, 8, 3, 6, 0, 1, 3, 7, 5, 5, 5, 4, 0, 3, 1, 0, 0, 6, 6, 9, 1, 2, 4, 9, 6, 3, 6, 5, 0, 4, 3, 2, 7, 2, 1, 0, 9, 5, 8, 1, 0, 7, 1, 4, 9, 8, 8, 3, 5, 2, 0, 3, 4, 6, 7, 1, 2, 0, 9, 3, 8, 4, 5, 8, 5, 8, 5, 0, 6, 0, 9, 8, 2, 9, 4, 1, 6, 5, 2, 6, 7, 3, 3, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The rotated Reuleaux triangle is not only a body of constant width, it is the minimum volume 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 Bernd Kawohl and Christof Weber, Meissner's Mysterious Bodies, Mathematical Intelligencer, Volume 33, Number 3, 2011, pp. 94-101. SwissEduc: Teaching and Learning Mathematics, Bodies of Constant Width (with informations on bodies of constant width like the rotated Reuleaux Triangle and others) FORMULA 2/3 * Pi - Pi^2 / 6 EXAMPLE 0.44946103... MATHEMATICA k1[x_] := Sqrt[1 - (x - Sqrt[3]/2)^2]; k2[x_] := Sqrt[1 - x^2] - 1/2; Pi * Integrate[k1[x]^2, {x, Sqrt[3]/2 - 1, 0}] + Pi * Integrate[k2[x]^2, {x, 0, Sqrt[3]/2}] CROSSREFS Cf. A102888, A137615, A137616, A137618. Sequence in context: A283919 A283670 A019627 * A023405 A160900 A035116 Adjacent sequences:  A137614 A137615 A137616 * A137618 A137619 A137620 KEYWORD cons,easy,nonn AUTHOR Christof Weber, Feb 04 2008 EXTENSIONS Link corrected by Christof Weber, Jan 06 2013 STATUS approved

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Last modified September 27 18:40 EDT 2020. Contains 337386 sequences. (Running on oeis4.)