Automated generation of readable proofs for constructive geometry statements with the mass point method

The existing readable machine proving methods deal with geometry problems using some geometric quantities. In this paper, we focus on the mass point method which directly deals with the geometric points rather than the geometric quantities. We propose two algorithms, Mass Point Method and Complex Mass Point Method, which can deal with the Hilbert intersection point statements in affine geometry and the linear constructive geometry statements in metric geometry respectively. The two algorithms are implemented in Maple as provers. The results of hundreds of non-trivial geometry statements run by our provers show that the mass point method is efficient and the machine proofs are human-readable.