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A066666
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Decimal expansion of area cut out by a rotating Reuleaux triangle.
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2
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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, 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, 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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| "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.
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REFERENCES
| Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009.
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LINKS
| Alexander Bogomolny, Shapes of constant width
Eric Weisstein's World of Mathematics, Reuleaux Triangle
Anonymous, Shape traced out by a rotating Reuleaux drill
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FORMULA
| Area = 2*Sqrt(3)+Pi/6 - 3 = 0.9877003907360534601319999...
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MATHEMATICA
| RealDigits[N[2*Sqrt[3] + Pi/6 - 3, 100]]
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CROSSREFS
| Cf. A060708, A060709.
Sequence in context: A132673 A107927 A019890 * A021905 A200688 A163243
Adjacent sequences: A066663 A066664 A066665 * A066667 A066668 A066669
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KEYWORD
| nonn,cons
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 11 2002
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