Automated generation of geometric theorems from images of diagrams

Abstract

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.

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Correspondence to Xiaoyu Chen.

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Chen, X., Song, D. & Wang, D. Automated generation of geometric theorems from images of diagrams. Ann Math Artif Intell 74, 333–358 (2015). https://doi.org/10.1007/s10472-014-9433-7

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Keywords

  • Theorem discovery
  • Pattern recognition
  • Image processing

Mathematics Subject Classification (2010)

  • 68T10
  • 68T15