Abstract
We present a complete method which can be used to produce short and human readable proofs for a class of constructive geometry statements in non-Euclidean geometries. The method is a substantial extension of the area method for Euclidean geometry. The method is an elimination algorithm which is similar to the variable elimination method of Wu used for proving geometry theorems. The difference is that instead of eliminating coordinates of points from general algebraic expressions, our method eliminates points from high level geometry invariants. As a result the proofs produced by our method are generally short and each step of the elimination has clear geometric meaning. A computer program based on this method has been used to prove more than 90 theorems from non-Euclidean geometries including many new ones. The proofs produced by the program are generally very short and readable.
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Yang, L., Gao, XS., Chou, SC., Zhang, JZ. (1998). Automated production of readable proofs for theorems in non-Euclidean geometries. In: Wang, D. (eds) Automated Deduction in Geometry. ADG 1996. Lecture Notes in Computer Science, vol 1360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022725
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DOI: https://doi.org/10.1007/BFb0022725
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