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%I #28 Mar 26 2013 16:13:59
%S 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,
%T 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,
%U 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
%N Decimal expansion of volume of the solid of revolution generated by a Reuleaux triangle rotated around one of its symmetry axes.
%C 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).
%D 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.
%H Bernd Kawohl and Christof Weber, <a href="http://www.fhnw.ch/personen/christof-weber/dateien/Kawohl_Weber_2011.pdf">Meissner's Mysterious Bodies</a>, Mathematical Intelligencer, Volume 33, Number 3, 2011, pp. 94-101.
%H SwissEduc: Teaching and Learning Mathematics, <a href="http://www.swisseduc.ch/mathematik/geometrie/gleichdick/index-en.html">Bodies of Constant Width</a> (with informations on bodies of constant width like the rotated Reuleaux Triangle and others)
%F 2/3 * Pi - Pi^2 / 6
%e 0.44946103...
%t 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}]
%Y Cf. A102888, A137615, A137616, A137618.
%K cons,easy,nonn
%O 0,1
%A _Christof Weber_, Feb 04 2008
%E Link corrected by _Christof Weber_, Jan 06 2013
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