Implementation of the Area Method
Julien Narboux
University of Strasbourg
This contribution consists in the formalization of a decision procedure for constructive theorems in Euclidean plane geometry. The procedure implemented is the area method by Chou, Gao and Zhang.
More than 100 example theorems are available among them:
- Ceva
- Desargues
- Pappus
- Menelaus
- Gauss line
- Euler line
- Centroïd
- Pascal
- Napoleon
More information about this implementation is available at :
http://dpt-info.u-strasbg.fr/~narboux/area_method.html
History:
2004 : implementation of the method for affine plane geometry
2009 : extension of the implementation to deal with euclidean geometry
References:
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Chou, Gao and Zhang - Machine Proofs in Geometry, Automated Production of Readable Proofs for Geometry Theorems, World Scientific 1994.
Julien Narboux - A decision procedure for geometry in Coq, Proceedings of TPHOLs'2004,Slind Konrad and Bunker Annett and Gopalakrishnan Ganesh editors, LNCS 3223, Springer-Verlag 2004.
Julien Narboux - Thèse : Formalisation et automatisation du raisonnement géométrique, 2006.
Predrag Janicic and Julien Narboux, and Pedro Quaresma - The Area Method : a recapitulation, submitted, 2009.