OFFSET
0,1
COMMENTS
With offset 1 this is the decimal expansion of 2*sqrt(Pi) = 3.544907..., which is the smallest possible perimeter index eta=P/sqrt(A) of all figures (not necessarily connected) in the Euclidean plane with a continuous boundary of length P (perimeter) enclosing a finite area A. The smallest value is attained only by a Euclidean planar disk. For example, eta=4 for squares, eta=2(sqrt(a/b)+sqrt(b/a))>=4 for aXb rectangles, and eta=4.559014... (A268604) for equilateral triangles. - Stanislav Sykora, Feb 08 2016
LINKS
FORMULA
sqrt(Pi)/5 = sqrt(4 * Pi)/10.
Equals -Gamma(-1/2)/10, where Gamma is Euler's gamma function. - Lee A. Newberg, Mar 05 2024
EXAMPLE
0.3544907701811...= 0.2*A002161.
MATHEMATICA
RealDigits[Sqrt[Pi]/5, 10, 100][[1]] (* Alonso del Arte, Jun 10 2012 *)
PROG
(PARI) sqrt(Pi)/5 \\ Charles R Greathouse IV, Sep 28 2022
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved