ABSTRACT
In 1947 Marshall Hall [7] proved that the set of numbers which can be written as a sum of two numbers whose partial quotients, in their continued fraction expansion, does not exceed 4, contains an interval of length greater than 1. Cassels [4] subsequently found a simpler proof, but this requires a weaker upper bound on the size of the partial quotients. It follows from Hall’s result that the Lagrange and Markoff spectra are continuous from some point on. This portion of these spectra is now known as Hall’s ray.
