A330934 Decimal expansion of the area of a sofa that can be moved around a 90-degree turn both to the right and to the left in a hallway of unit width.

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

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

Table of n, a(n) for n=1..105.

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

Cf. A086118, A128463.

Sequence in context: A200698 A013661 A209273 * A019174 A019166 A058158

Adjacent sequences: A330931 A330932 A330933 * A330935 A330936 A330937

Keyword

nonn,cons

Author

Rick L. Shepherd, Jan 03 2020

Status

approved