A066666 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

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

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

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

Anonymous, Shape traced out by a rotating Reuleaux drill.

Alexander Bogomolny, Shapes of constant width.

Eric Weisstein's World of Mathematics, Reuleaux Triangle.

FORMULA

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

MATHEMATICA

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

PROG

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