Abstract
How to automatically generate short and easy-to-understand proofs for geometric theorems has long been an issue of concern in mathematics education. A novel automated geometric theorem proving method based on complex number identities is proposed in this paper, which acts as a bridge between geometry and algebra. According to the proposed method, the geometric relations in the given proposition are first transformed into a complex number expression, then the complex number identity is generated by the elimination method; finally, the closure property under all four operations of real numbers is employed to prove the proposition. A test on more than 300 geometric problems shows that the proposed method is highly effective, and the corresponding proofs are short, with obvious geometric meaning.
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This work was financially supported by the Research Funds from the National Natural Science Foundation of China (Grant No. 62077019).
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Peng, X., Zhang, J., Chen, M. et al. Self-evident Automated Geometric Theorem Proving Based on Complex Number Identity. J Autom Reasoning 67, 38 (2023). https://doi.org/10.1007/s10817-023-09688-w
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DOI: https://doi.org/10.1007/s10817-023-09688-w