计算机工程2025，Vol.51Issue(7)：78-89,12.DOI:10.19678/j.issn.1000-3428.0068959
基于向量恒等式的几何证明题自动生成方法
Approach for Automated Generation of Geometric Proof Problems Based on Vector Identity
摘要
Abstract
Automated generation of geometry proof problems is a prominent research area in the field of intelligent education.Current methods commonly employ automated geometric reasoning techniques to discover new geometric relationships based on the original geometric relations of an existing question,thereby synthesizing new relationships.However,the problems generated by these methods lack novelty because the geometric relationships they contain can be inferred from the original geometric relationships of the input problem.To address this limitation,this study proposes an approach for generating new problems by recombining the geometric relationships of two existing problems.By introducing the theory of vector identity equation,a theoretical foundation is established for representing geometric relationships and determining whether geometric relationships from different problems can be reorganized to form new problems.Consequently,algorithms are developed to automatically extract geometric relationships from existing problems and recombine them to generate novel problem instances.Experimental analysis and expert evaluation demonstrate the feasibility of the proposed method in terms of operational performance and educational application.Notably,under the same input conditions,the proposed method can generate more novel problems than existing methods.关键词
习题自动生成/几何证明题/向量恒等式/几何定理自动发现Key words
automated generation of problems/geometry proof problems/vector identity equation/automated discovery of geometric theorems分类
信息技术与安全科学引用本文复制引用
李雷,陈矛,彭翕成..基于向量恒等式的几何证明题自动生成方法[J].计算机工程,2025,51(7):78-89,12.基金项目
国家自然科学基金(62077019) （62077019）
西北师范大学青年教师科研能力提升计划项目(NWNU-SKQN2023-36). （NWNU-SKQN2023-36）
