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

1,2

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).

Links

Table of n, a(n) for n=1..97.

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

Example

1.975592884781500515916465258513589346516747916843208984560424391176647...

Mathematica

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

Prog

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

Crossrefs

Cf. A307234.

Sequence in context: A222129 A188141 A244667 * A194554 A065467 A021839

Adjacent sequences: A307232 A307233 A307234 * A307236 A307237 A307238

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