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Automated production of readable proofs for theorems in non-Euclidean geometries

  • Lu Yang
  • Xiao-Shan Gao
  • Shang-Ching Chou
  • Jing-Zhong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1360)

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.

Keywords

Theorem Prove Elliptic Geometry Hyperbolic Geometry Geometric Quantity Automate Theorem Prove 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Lu Yang
    • 1
  • Xiao-Shan Gao
    • 2
  • Shang-Ching Chou
    • 3
  • Jing-Zhong Zhang
    • 1
  1. 1.Chengdu Institute of Computer ApplicationsAcademia SinicaChina
  2. 2.Institute of Systems ScienceAcademia SinicaChina
  3. 3.Department of Computer ScienceThe Wichita State UniversityWichita

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