A307235 Decimal expansion of sqrt(2) + sqrt((3-3*sqrt(3)+Pi)/3).

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

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 4 pieces of equal area after making certain assumptions about the cuts (compare A307234).

Examples

			1.975592884781500515916465258513589346516747916843208984560424391176647...
		

Links

• Eduard Baumann, Dissection of regular polygons in n equal area pieces with minimal cut length
• Zhao Hui Du, Picture showing how to cut the square into 4 pieces
• Paolo Licheri, f006 Tagliare una torta, (Cut a Cake, in Italian).
• Yi Yang, A Chinese BBS
• Index entries for transcendental numbers

Crossrefs

Cf. A307234.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2) + Sqrt((Pi(R)+3-3*Sqrt(3))/3); // G. C. Greubel, Jul 02 2019

Mathematica

RealDigits[Sqrt[2] + Sqrt[(Pi+3-3*Sqrt[3])/3], 10, 100][[1]] (* G. C. Greubel, Jul 02 2019 *)

PARI

default(realprecision, 100); sqrt(2) + sqrt((Pi+3-3*sqrt(3))/3) \\ G. C. Greubel, Jul 02 2019

Sage

numerical_approx(sqrt(2) + sqrt((pi+3-3*sqrt(3))/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