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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
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
Sequence in context: A201894 A023400 A153637 * A340866 A021338 A021889
KEYWORD
cons,easy,nonn
AUTHOR
Christof Weber, Feb 04 2008
STATUS
approved

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