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%I #25 May 22 2023 08:57:12
%S 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,
%T 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,
%U 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
%N Decimal expansion of surface area 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 surface of constant width, it is the minimum area 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.mi.uni-koeln.de/mi/Forschung/Kawohl/kawohl/pub100.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">Gleichdick - Koerper konstanter Breite</a> (in German and English)
%F Equals 2*Pi - Pi^2 /3.
%e 2.99331717348313360398045643326695538995643899633661...
%t 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}]
%t RealDigits[2*Pi - Pi^2/3, 10, 120][[1]] (* _Amiram Eldar_, May 22 2023 *)
%Y Cf. A102888, A137615, A137616, A137617.
%K cons,easy,nonn
%O 1,1
%A _Christof Weber_, Feb 04 2008