On the Inhomogeneous Hall's Ray of Period-One Quadratics

L{9) := {M(0,7) : 7 e R, 7 0 Z+0Z} C [0, |] . (1-1) Arguably, the inhomogeneous analogue of the classical Lagrange spectrum L = {M(0,O)~ : 0 G R} should be the set of M(0,7)~ rather than the set of M(0,7), but in order to work with more easily illustrated bounded intervals we decided to avoid the unnecessary complication of taking reciprocals (it is of course trivial to translate our results should the reader prefer the convention of inverting everything). We are interested here in the largest interval [0, c(0)] contained in this spectrum, This work was performed while Pinner was at the University of Northern British Columbia, Prince George, BC. c(0) := SUp{c : [0, c] C L(0)} ,