A307235 - OEIS

%I #52 Oct 01 2022 00:18:38

%S 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,

%T 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,

%U 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

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

%C 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).

%H Eduard Baumann, <a href="http://www.baumanneduard.ch/EqAreaOverview.htm">Dissection of regular polygons in n equal area pieces with minimal cut length</a>

%H Zhao Hui Du, <a href="/A307235/a307235.png">Picture showing how to cut the square into 4 pieces</a>

%H Paolo Licheri, <a href="http://web.tiscalinet.it/paololicheri/figure/f006x.htm">f006 Tagliare una torta</a>, (Cut a Cake, in Italian).

%H Yi Yang, <a href="https://translate.google.com/translate?hl=&amp;sl=zh-CN&amp;tl=en&amp;u=https%3A%2F%2Fbbs.emath.ac.cn%2Fforum.php%3Fmod%3Dredirect%26goto%3Dfindpost%26ptid%3D2745%26pid%3D33264%26fromuid%3D20">A Chinese BBS</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1.975592884781500515916465258513589346516747916843208984560424391176647...

%t RealDigits[Sqrt[2] + Sqrt[(Pi+3-3*Sqrt[3])/3], 10, 100][[1]] (* _G. C. Greubel_, Jul 02 2019 *)

%o (PARI) default(realprecision, 100); sqrt(2) + sqrt((Pi+3-3*sqrt(3))/3) \\ _G. C. Greubel_, Jul 02 2019

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2) + Sqrt((Pi(R)+3-3*Sqrt(3))/3); // _G. C. Greubel_, Jul 02 2019

%o (Sage) numerical_approx(sqrt(2) + sqrt((pi+3-3*sqrt(3))/3), digits=100) # _G. C. Greubel_, Jul 02 2019

%Y Cf. A307234.

%K nonn,cons

%O 1,2

%A _Zhao Hui Du_, Mar 30 2019

%E Terms a(32) onward added by _G. C. Greubel_, Jul 02 2019

%E Edited by _N. J. A. Sloane_, Aug 16 2019