|
%I #18 May 07 2018 03:54:39
%S 2,2,1,9,5,3,1,6,6,8,8,7,1,9,7
%N Decimal expansion of area of Gerver's sofa.
%C What is the sofa of greatest area S which can be moved around a right-angled hallway of unit width? Hammersley bounded this by A086118). Gerver (1992) found a sofa with larger area and provided arguments indicating that it is either optimal or close to it. The boundary of Gerver's sofa is a complicated shape composed of 18 arcs.
%D S. R. Finch, Moving Sofa Constant, Sect. 8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.
%H J. L. Gerver, <a href="https://doi.org/10.1007/BF02414066">On Moving a Sofa Around a Corner</a>, Geometriae Dedicata 42, 267-283, 1992.
%H Yoav Kallus and Dan Romik, <a href="https://arxiv.org/abs/1706.06630">Improved upper bounds in the moving sofa problem</a>, arXiv preprint arXiv:1706.06630 [math.MG], 2017.
%H Dan Romik, <a href="https://arxiv.org/abs/1606.08111">Differential equations and exact solutions in the moving sofa problem</a>, arXiv:1606.08111 [math.DG], 2016.
%H 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 (2017): 1-15.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MovingSofaProblem.html">Moving Sofa Problem</a>.
%e 2.21953166887197...
%Y Cf. A086118.
%K cons,nonn,more
%O 1,1
%A _Jonathan Vos Post_, May 05 2007
|
