OFFSET

1,2

COMMENTS

According to Dan Romik, this may be the largest possible area of such a sofa. He gives the closed-form formula below for the area of this shape which consists of "18 distinct pieces, each of which is given by a separate formula obtained as the solution of some differential equation." See the D. Romik link for a picture of this shape and animations of this and related sofas.

LINKS

Dan Romik, The Moving Sofa Problem.

Dan Romik, Differential equations and exact solutions in the moving sofa problem, Experimental Mathematics, Vol. 27, No. 3 (2018), pp. 316-330; arXiv preprint, arXiv:1606.08111 [math.DG], 2016.

Eric Weisstein's World of Mathematics, Moving Sofa Problem.

Wikipedia, Moving sofa problem.

FORMULA

Equals (3 + 2*sqrt(2))^(1/3) + (3 - 2*sqrt(2))^(1/3) - 1 + atan(((sqrt(2) + 1)^(1/3) - (sqrt(2) - 1)^(1/3))/2) [D. Romik].

EXAMPLE

1.644955218425440851668809347600633685194252864098962636889345708010329...

MATHEMATICA

RealDigits[(3 + 2*Sqrt[2])^(1/3) + (3 - 2*Sqrt[2])^(1/3) - 1 + ArcTan[((Sqrt[2] + 1)^(1/3) - (Sqrt[2] - 1)^(1/3))/2], 10, 120][[1]] (* Amiram Eldar, Jun 18 2023 *)

PROG

(PARI) {default(realprecision, 200);

my(sr2 = sqrt(2)); (3+2*sr2)^(1/3) + (3-2*sr2)^(1/3) - 1 + atan(((sr2+1)^(1/3) - (sr2-1)^(1/3))/2)}

CROSSREFS

KEYWORD

nonn,cons

AUTHOR

Rick L. Shepherd, Jan 03 2020

STATUS

approved