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

Author

Robert G. Wilson v, Jan 11 2002

Keywords

• nonn
• cons

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

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.3.1, p. 490.
• Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009.

Links

• Anonymous, Shape traced out by a rotating Reuleaux drill.
• Alexander Bogomolny, Shapes of constant width.
• Eric Weisstein's World of Mathematics, Reuleaux Triangle.

Crossrefs

Cf. A060708, A060709.

Programs

Mathematica

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

PARI

2*sqrt(3) + Pi/6 - 3 \\ Stefano Spezia, Dec 21 2024

Formula

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