A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering
Journal of Automated Reasoning
Proceedings of the 2009 ACM symposium on Applied Computing
The 2009 ACM Symposium on Applied Computing
Formalizing Desargues' theorem in Coq using ranks
Proceedings of the 2009 ACM symposium on Applied Computing
Interrogating witnesses for geometric constraint solving
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Using the witness method to detect rigid subsystems of geometric constraints in CAD
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry
Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry
Cancellation patterns in automatic geometric theorem proving
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
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Search methods provide short and human readable proofs, i.e. with few algebra, of most of the theorems of the Euclidean plane. They are less succesful and convincing for incidence theorems of projective geometry, which has received less attention up to now. This is due to the fact that basic notions, like angles and distances, which are relevant for Euclidean geometry, are no more relevant for projective geometry. This article suggests that search methods can also provide short and human readable proofs of incidence theorems of projective geometry with well chosen notions, rules or lemmas. This article proposes such lemmas, and show that they indeed permit to find by hand short proofs of some theorems of projective geometry.