A137617 - OEIS

%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