Abstract
In this thesis, we develop methods making use of the Gröbner system to solve problems in projective geometry including automatic theorem proving, automatic theorem discovering and three dimensional visualization. Automatic theorem proving aims to use computer to translate geometric statements and perform verification to check if a statement can imply another statement. As for automatic theorem discovery, one attempts to use computer to find out the missing criteria for a hypothesis to be possibly true. Lastly, three dimensional visualization include the method of projecting 3D objects on to a 2D screen of a display. This paper suggests a method using Gröbner basis on these areas and give relevant examples.