A066666 Decimal expansion of area cut out by a rotating Reuleaux triangle.

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

Offset

0,1

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.

References

Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009.

Links

Table of n, a(n) for n=0..99.

Alexander Bogomolny, Shapes of constant width

Eric Weisstein's World of Mathematics, Reuleaux Triangle

Anonymous, Shape traced out by a rotating Reuleaux drill

Formula

Area = 2*Sqrt(3)+Pi/6 - 3 = 0.9877003907360534601319999...

Mathematica

RealDigits[N[2*Sqrt[3] + Pi/6 - 3, 100]]

Crossrefs

Cf. A060708, A060709.

Sequence in context: A363249 A107927 A019890 * A369763 A347201 A021905

Adjacent sequences: A066663 A066664 A066665 * A066667 A066668 A066669

Keyword

nonn,cons

Author

Robert G. Wilson v, Jan 11 2002

Status

approved