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

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Abstract

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.

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Authors and Affiliations

  1. National Engineering Research Center for E-Learning, Central China Normal University, Wuhan, 430079, China

    Jingzhong Zhang, Xicheng Peng & Mao Chen

  2. Institute of Computational Science and Technology, Guangzhou University, Guangzhou, 510006, China

    Jingzhong Zhang

  3. Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, 610041, China

    Jingzhong Zhang

Authors
  1. Jingzhong Zhang
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  2. Xicheng Peng
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  3. Mao Chen
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Corresponding author

Correspondence to Mao Chen.

Additional information

This work was supported in part by the National Key Research and Development Program of China under Grant No. 2017YFB1401302, the National Natural Science Foundation of China under Grant No. 41671377.

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Zhang, J., Peng, X. & Chen, M. Self-evident Automated Proving Based on Point Geometry from the Perspective of Wu’s Method Identity. J Syst Sci Complex 32, 78–94 (2019). https://doi.org/10.1007/s11424-019-8350-6

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  • DOI: https://doi.org/10.1007/s11424-019-8350-6

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