Proving Geometric Problem by Adding Auxiliary Lines-Based on Hypothetical Test

Abstract

With the continuous development on computer science and technology, people have begun to use automatic reasoning systems to solve some logical mathematical proof problems. The traditional reasoning system can use the finite conditions to verify the conclusion of the problem, to achieve the effect of proving geometric problems. However, there is no unified standard for the proof of plane geometric problems, it is impossible to use formulas to prove directly. More importantly, some problems do not contain all the proof conditions, and have to add auxiliary lines to prove. However, there is still no unified standard for drawing auxiliary lines in the mathematical world. Therefore, there is no corresponding template for reference to add the function of automatic drawing auxiliary lines in the automatic reasoning system, which has a certain challenge and research value. Because the mathematical field can not summarize the standard implementation of auxiliary line construction, the research on automatic addition of auxiliary line in computer field is relatively less, and the common addition methods are mainly based on model classification or exhaustive. But these traditional algorithms have the problems of low efficiency or unlimited growth of problem scale. The main research goal of this paper is to optimize the auxiliary line adding algorithm based on exhaustive method. This paper proposes an auxiliary line adding algorithm for plane geometry problems based on hypothesis testing, which makes it more efficient in solving complex elementary mathematical and geometric problems, and avoids the problem of unlimited growth of traditional algorithm.