It is well known that for a quadratic form
Q in 3 or more variables, with real or complex
coefficients, which is nondegenerate, indefinite
and not a scalar multiple of a form with rational
coefficients, the set of values of Q over points
with integral coordinates (Gaussian integers in
the complex case) is dense among all numbers
(real or complex respectively). The analoguous
statement is not true for binary quadratic forms, whether over reals or complex numbers. The question in this case can be related to continued
fraction expansions, and the results on the theme
will be discussed using the classical theory of continued fractions in the real case and some
newly obtained results on continued fraction
expansions in the case of complex numbers.