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%I #9 Mar 30 2012 17:30:38
%S 9,8,7,7,0,0,3,9,0,7,3,6,0,5,3,4,6,0,1,3,1,9,9,9,9,1,3,5,5,8,3,2,8,5,
%T 4,7,9,1,8,4,7,2,0,7,4,1,8,3,2,7,8,8,9,2,9,4,0,7,7,1,3,9,0,9,5,5,1,6,
%U 8,7,6,8,1,9,8,6,3,4,9,0,7,2,6,6,9,6,4,8,4,4,4,0,4,8,4,9,9,9,6,0
%N Decimal expansion of area cut out by a rotating Reuleaux triangle.
%C "Yes - there are shapes of constant width other than the circle. No - you can't drill square holes. But saying this was not just an attention catcher. As the applet on the right illustrates, you can drill holes that are almost square - drilled holes whose border includes straight line segments!" - Bogomolny. The Java applet shows it in its three versions.
%D Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009.
%H Alexander Bogomolny, <a href="http://www.cut-the-knot.org/do_you_know/cwidth.shtml">Shapes of constant width</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ReuleauxTriangle.html">Reuleaux Triangle</a>
%H Anonymous, <a href="http://hypo.ge-dip.etat-ge.ch/www/math/gif/reuleauxt.gif">Shape traced out by a rotating Reuleaux drill</a>
%F Area = 2*Sqrt(3)+Pi/6 - 3 = 0.9877003907360534601319999...
%t RealDigits[N[2*Sqrt[3] + Pi/6 - 3, 100]]
%Y Cf. A060708, A060709.
%K nonn,cons
%O 0,1
%A _Robert G. Wilson v_, Jan 11 2002
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