Diophantine approximation in the field

In this paper, we consider the approximation spectrum w.r.t. the field . The smallest limit point of this spectrum is found to be c0=1.78863819… , where c0 belongs to a real quadratic extension of , and a complete description of the spectrum below and slightly above c0 is given. The result is obtained by using a continued fraction like algorithm which has the same properties as ordinary continued fractions.