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

Author

Zhao Hui Du, Mar 30 2019

Keywords

• nonn
• cons

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).

Examples

			2.5021129304271862327055851940086922513958756262307745535319011955...
		

Links

• 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.

Crossrefs

Cf. A307234, A307235, A307238.

Programs

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

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 *)

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

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

Extensions

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

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