Abstract
Automated discovery of geometric theorems has attracted considerable attention from the research community. In this paper, a new method is proposed to discover geometric theorems automatically. This method first generates vector equations based on given geometric relations about a geometric figure and then transforms the vector equations into a system of homogeneous linear equations; after computing the determinants of the coefficient matrices corresponding to the system of equations, the elimination method is applied to obtain a large number of geometric relationships. The test on more than 200 geometric problems shows that the geometric relationships discovered automatically by the proposed method are of obvious geometric meaning.
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Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (Grant No. 62077019, 41671377), National Key R&D Program of China (Grant No. 2017YFB1401300). We are grateful to the reviewers for their useful comments and suggestions which helped us to significantly improve the paper.
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Peng, X., Chen, Q., Zhang, J. et al. Automated Discovery of Geometric Theorems Based on Vector Equations. J Autom Reasoning 65, 711–726 (2021). https://doi.org/10.1007/s10817-021-09591-2
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DOI: https://doi.org/10.1007/s10817-021-09591-2