Automated reasoning in geometry theorem proving with Prolog
Journal of Automated Reasoning
Using Gröbner bases to reason about geometry problems
Journal of Symbolic Computation
Geometry theorem proving using Hilbert's Nullstellensatz
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Realization of a geometry-theorem proving machine
Computers & thought
A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering
Journal of Automated Reasoning
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Automated Production of Readable Proofs for Theorems in Non-Euclidian Geometries
Selected Papers from the International Workshop on Automated Deduction in Geometry
Higher-Order Intuitionistic Formalization and Proofs in Hilbert's Elementary Geometry
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
An Introduction to Geometry Expert
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
The Thirteen Books of Euclid's Elements, Books 1 and 2
The Thirteen Books of Euclid's Elements, Books 1 and 2
Formal certification of a compiler back-end or: programming a compiler with a proof assistant
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Graphical User Interface for Formal Proofs in Geometry
Journal of Automated Reasoning
Formalizing Desargues' theorem in Coq using ranks
Proceedings of the 2009 ACM symposium on Applied Computing
Geometry Constructions Language
Journal of Automated Reasoning
Automatic verification of regular constructions in dynamic geometry systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Mechanical theorem proving in Tarski's geometry
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Visually Dynamic Presentation of Proofs in Plane Geometry
Journal of Automated Reasoning
Visually Dynamic Presentation of Proofs in Plane Geometry
Journal of Automated Reasoning
Formalizing projective plane geometry in Coq
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Integrating dynamic geometry software, deduction systems, and theorem repositories
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
GCLC: a tool for constructive euclidean geometry and more than that
ICMS'06 Proceedings of the Second international conference on Mathematical Software
System description: GCLCprover + geothms
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Thousands of geometric problems for geometric theorem provers (TGTP)
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Formalization of wu's simple method in coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
A case study in formalizing projective geometry in Coq: Desargues theorem
Computational Geometry: Theory and Applications
Towards understanding triangle construction problems
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
The web geometry laboratory project
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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The area method for Euclidean constructive geometry was proposed by Chou, Gao and Zhang in the early 1990's. The method can efficiently prove many non-trivial geometry theorems and is one of the most interesting and most successful methods for automated theorem proving in geometry. The method produces proofs that are often very concise and human-readable. In this paper, we provide a first complete presentation of the method. We provide both algorithmic and implementation details that were omitted in the original presentations. We also give a variant of Chou, Gao and Zhang's axiom system. Based on this axiom system, we proved formally all the lemmas needed by the method and its soundness using the Coq proof assistant. To our knowledge, apart from the original implementation by the authors who first proposed the method, there are only three implementations more. Although the basic idea of the method is simple, implementing it is a very challenging task because of a number of details that has to be dealt with. With the description of the method given in this paper, implementing the method should be still complex, but a straightforward task. In the paper we describe all these implementations and also some of their applications.