  We prove the Oppenheim conjecture for indefinite ternary diagonal forms of
the type $x^{2}+y^{2} -\beta^{2} z^{2}$ where $ \beta $ is an irrational
number. Our method is explicit in the sense that we are able to construct a
solution to the problem and we obtain an effective bound on the solution. The
method is geometrical and is based on elementary metric diophantine
approximation.
