(untitled) (International journal of artificial intelligence, 2025)
This article examines the role of projective geometry in solving elementary geometry problems. Projective geometry, a branch of mathematics focusing on properties invariant under projection, provides powerful tools and perspectives that simplify and generalize classical geometric constructions and proofs. By extending the Euclidean plane to include points at infinity and employing concepts such as cross-ratio and harmonic division, projective methods enable elegant solutions to problems involving collinearity, concurrency, and incidence relations. The paper illustrates key projective geometry principles and demonstrates their applications through typical elementary geometry problems, highlighting how projective approaches can unify and enrich traditional Euclidean techniques. This study aims to enhance the understanding and problem-solving skills of students and educators in geometry.