%I #33 Mar 05 2024 16:33:10

%S 3,5,4,4,9,0,7,7,0,1,8,1,1,0,3,2,0,5,4,5,9,6,3,3,4,9,6,6,6,8,2,2,9,0,

%T 3,6,5,5,9,5,0,9,8,9,1,2,2,4,4,7,7,4,2,5,6,4,2,7,6,1,5,5,7,9,7,0,5,8,

%U 2,2,5,6,9,1,8,2,0,6,4,3,6,2,7,4,9,9,0,1,3,1,3,4,7,7,0,8,9,3,3

%N Decimal expansion of sqrt(Pi)/5.

%C 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

%H Ivan Panchenko, <a href="/A019707/b019707.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F sqrt(Pi)/5 = sqrt(4 * Pi)/10.

%F Equals -Gamma(-1/2)/10, where Gamma is Euler's gamma function. - _Lee A. Newberg_, Mar 05 2024

%e 0.3544907701811...= 0.2*A002161.

%t RealDigits[Sqrt[Pi]/5, 10, 100][[1]] (* _Alonso del Arte_, Jun 10 2012 *)

%o (PARI) sqrt(Pi)/5 \\ _Charles R Greathouse IV_, Sep 28 2022

%Y Cf. A000796, A002161, A087198, A268604.

%K nonn,easy,cons

%O 0,1

%A _N. J. A. Sloane_