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

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, 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, 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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..96.

Simon Cox, Minimal perimeter enclosing N cells of equal area with N no more than 42

Zhao Hui Du, Picture showing how square is cut into 5 pieces

M. Gardner, The Mathemagician and Pied Puzzler, Problem H14.

Example

2.5021129304271862327055851940086922513958756262307745535319011955...

Mathematica

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 *)

Prog

(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
(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
(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

Crossrefs

Cf. A307234, A307235, A307238.

Sequence in context: A005671 A343605 A296047 * A127863 A006891 A054675

Adjacent sequences: A307234 A307235 A307236 * A307238 A307239 A307240

Keyword

nonn,cons

Author

Zhao Hui Du, Mar 30 2019

Extensions

Terms a(32) onward added by G. C. Greubel, Jul 02 2019

Edited by N. J. A. Sloane, Aug 16 2019

Status

approved