Automated Proving Particle Geometry Theorems Involving Ratios Of Particles Volume

Particle geometric theorem proving has always been a research hotspot in the automatic reasoning area.Its research methods and results have obvious application value.In recent years,according to theorems and properties of particle geometry,researchers have provided the particle method,which is based to implement the particle geometry theorem provers.Nowadays,the particle method still has some issues.For example,the geometric theorems involving length and area can not be proved,the conclusion can not be directly derived through the elimination point,and the output is less readable.In order to solve these issues,this paper provides a novel automated proving particle geometry theorem,the volume-type particle elimination.This method not only proves the volume ratio type of particle geometry theorems,but also derives the particle relations.Due to introducing rules of particle volume,this method can not only simultaneously simplify and eliminate points,but also directly derive the conclusion.Therefore,the proof process of output is more similar to the traditional problem-solving process.And each step of the proofs has clear geometric meaning.With the help of eliminating points,the proof process of output is more shorter,and the readability is more satisfactory.Based on the new proposed method,a prover PMP of particle geometry theorem is designed and implemented through Matlab.The program has proved more than thirty particle geometry theorems involving ratios of particles volume.The experimental results show that the prover can not only automatically generate concise and readable proof,but also has satisfactory efficiency.It is expected that the prover PMP can be a powerful tool for proving particle geometry theorems,and it can help to study the geometry theorem machine proof or develop education software in future.