cp's OEIS Frontend

A307237 Decimal expansion of 2 + (-6 + (1+sqrt(3))*Pi)*sqrt(2/(15*(2*Pi-3 +(Pi-3)*sqrt(3)))).

%I A307237 #38 Jul 11 2022 23:36:00
%S A307237 2,5,0,2,1,1,2,9,3,0,4,2,7,1,8,6,2,3,2,7,0,5,5,8,5,1,9,4,0,0,8,6,9,2,
%T A307237 2,5,1,3,9,5,8,7,5,6,2,6,2,3,0,7,7,4,5,5,3,5,3,1,9,0,1,1,9,5,5,0,2,8,
%U A307237 0,5,9,4,0,9,4,1,9,3,1,3,5,8,0,1,1,2,0,6,5,1,5,6,8,2,8,6
%N A307237 Decimal expansion of 2 + (-6 + (1+sqrt(3))*Pi)*sqrt(2/(15*(2*Pi-3 +(Pi-3)*sqrt(3)))).
%C A307237 This is claimed to be the minimal cut length required to cut a unit square into 5 pieces of equal area after making certain assumptions about the cuts (compare A307234).
%H A307237 Simon Cox, <a href="http://users.aber.ac.uk/sxc/two_d_clusters.html">Minimal perimeter enclosing N cells of equal area with N no more than 42</a>
%H A307237 Zhao Hui Du, <a href="/A307237/a307237.png">Picture showing how square is cut into 5 pieces</a>
%H A307237 M. Gardner, <a href="http://plouffe.fr/simon/Phys%20et%20Math/Martin%20Gardner%20-%20Mathemagics%20&amp;%20Math%20Puzzles.pdf">The Mathemagician and Pied Puzzler</a>, Problem H14.
%e A307237 2.5021129304271862327055851940086922513958756262307745535319011955...
%t A307237 RealDigits[2 +(-6 +(1+Sqrt[3])*Pi)*Sqrt[2/(15*(2*Pi -3 +(Pi-3)*Sqrt[3]) )], 10, 100][[1]] (* _G. C. Greubel_, Jul 02 2019 *)
%o A307237 (PARI) default(realprecision, 100); 2 +(-6 +(1+sqrt(3))*Pi)*sqrt(2/(15*(2*Pi-3 +(Pi-3)*sqrt(3)))) \\ _G. C. Greubel_, Jul 02 2019
%o A307237 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2 +(-6 +(1+Sqrt(3))*Pi(R))*Sqrt(2/(15*(2*Pi(R)-3 +(Pi(R)-3)*Sqrt(3)))); // _G. C. Greubel_, Jul 02 2019
%o A307237 (Sage) numerical_approx(2 + (-6 + (1+sqrt(3))*pi)*sqrt(2/(15*(2*pi-3 +(pi-3)*sqrt(3)))), digits=100) # _G. C. Greubel_, Jul 02 2019
%Y A307237 Cf. A307234, A307235, A307238.
%K A307237 nonn,cons
%O A307237 1,1
%A A307237 _Zhao Hui Du_, Mar 30 2019
%E A307237 Terms a(32) onward added by _G. C. Greubel_, Jul 02 2019
%E A307237 Edited by _N. J. A. Sloane_, Aug 16 2019