Journal of Systems Science and Complexity

, Volume 32, Issue 1, pp 78–94 | Cite as

Self-evident Automated Proving Based on Point Geometry from the Perspective of Wu’s Method Identity

  • Jingzhong Zhang
  • Xicheng Peng
  • Mao ChenEmail author


The algebraic methods represented by Wu’s method have made significant breakthroughs in the field of geometric theorem proving. Algebraic proofs usually involve large amounts of calculations, thus making it difficult to understand intuitively. However, if the authors look at Wu’s method from the perspective of identity,Wu’s method can be understood easily and can be used to generate new geometric propositions. To make geometric reasoning simpler, more expressive, and richer in geometric meaning, the authors establish a geometric algebraic system (point geometry built on nearly 20 basic properties/formulas about operations on points) while maintaining the advantages of the coordinate method, vector method, and particle geometry method and avoiding their disadvantages. Geometric relations in the propositions and conclusions of a geometric problem are expressed as identical equations of vector polynomials according to point geometry. Thereafter, a proof method that maintains the essence of Wu’s method is introduced to find the relationships between these equations. A test on more than 400 geometry statements shows that the proposed proof method, which is based on identical equations of vector polynomials, is simple and effective. Furthermore, when solving the original problem, this proof method can also help the authors recognize the relationship between the propositions of the problem and help the authors generate new geometric propositions.


Geometry algebra point geometry proof method based on identical equations vector geometry Wu’s method 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Engineering Research Center for E-LearningCentral China Normal UniversityWuhanChina
  2. 2.Institute of Computational Science and TechnologyGuangzhou UniversityGuangzhouChina
  3. 3.Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChongqingChina

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