The Application of Determining Sets to Projective Configurations

An \(n_3\)-configuration in the real projective plane is a configuration consisting of \(n\) points and \(n\) lines such that every point is on three lines and every line contains three points. Determining sets are used to construct drawings of arbitrary \(n_3\)-configurations in the plane, such that one line is represented as a circle. It is proved that the required determining set always exists, and that such a drawing is always possible. This is applied to the problem of deciding when a particular configuration is coordinatizable.