Automatic generation of geometric base sequences

Abstract

How to use computers to effectively solve geometric computation problems is one important focus in the development of geometry. In this paper, we introduce a new method to solve geometric problems with a geometric method. We establish a set of geometric bases and generate sequences of these geometric bases automatically with forward-reasoning. The geometric base sequence is a new description of the solution of geometric problems which is more readable than the solution generated by algebra methods. Moreover, we modify the hidden Markov chain model to avoid information explosion. Experimental results indicate that our method can be used to generate the sequences efficiently.