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 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 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 2 * Pi - Pi^2 /3. EXAMPLE 2.99331717... 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}] CROSSREFS Cf. A102888, A137615, A137616, A137617. Sequence in context: A201894 A023400 A153637 * A021338 A021889 A309927 Adjacent sequences:  A137615 A137616 A137617 * A137619 A137620 A137621 KEYWORD cons,easy,nonn AUTHOR Christof Weber, Feb 04 2008 STATUS approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)