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- [1] Self-evident Automated Geometric Theorem Proving Based on Complex Number IdentityJournal of Automated Reasoning, 2023, 67Xicheng PengJingzhong ZhangMao ChenSannyuya Liu
Self-evident Automated Geometric Theorem Proving Based on Complex Number Identity
被引：0
|作者：
Peng, Xicheng
[1
]
Zhang, Jingzhong
[1
,2
]
Chen, Mao
[1
]
Liu, Sannyuya
[1
]
机构：
[1] Cent China Normal Univ, Natl Engn Lab Educ Big Data, Wuhan 430079, Peoples R China
[2] Guangzhou Univ, Inst Computat Sci & Technol, Guangzhou 510006, Peoples R China
基金：
中国国家自然科学基金;
关键词：
Complex number identity;
Self-evident automated proving;
Complex number geometry;
Geometric theorems;
Elimination method;
READABLE PROOFS;
GENERATION;
INVARIANTS;
D O I：
10.1007/s10817-023-09688-w
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ;
0812 ;
0835 ;
1405 ;
摘要：
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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页数：18
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