cp's OEIS Frontend

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.

%I A330934 #24 Feb 16 2025 08:33:59
%S A330934 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,
%T A330934 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,
%U A330934 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
%N 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.
%C A330934 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.
%H A330934 Dan Romik, <a href="http://math.ucdavis.edu/~romik/movingsofa/">The Moving Sofa Problem</a>.
%H A330934 Dan Romik, <a href="https://doi.org/10.1080/10586458.2016.1270858">Differential equations and exact solutions in the moving sofa problem</a>, Experimental Mathematics, Vol. 27, No. 3 (2018), pp. 316-330; <a href="https://arxiv.org/abs/1606.08111">arXiv preprint</a>, arXiv:1606.08111 [math.DG], 2016.
%H A330934 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MovingSofaProblem.html">Moving Sofa Problem</a>.
%H A330934 Wikipedia, <a href="https://en.wikipedia.org/wiki/Moving_sofa_problem">Moving sofa problem</a>.
%F A330934 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].
%e A330934 1.644955218425440851668809347600633685194252864098962636889345708010329...
%t A330934 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 *)
%o A330934 (PARI) {default(realprecision, 200);
%o A330934 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)}
%Y A330934 Cf. A086118, A128463.
%K A330934 nonn,cons
%O A330934 1,2
%A A330934 _Rick L. Shepherd_, Jan 03 2020