Automated Generation of Geometric Theorems from Images of Diagrams

TL;DR

This paper presents an automated method to generate geometric theorems from images of diagrams by recognizing geometric objects, verifying relations, and deriving theorems through algebraic computation, aiding knowledge management and education.

Contribution

It introduces a novel approach combining image recognition, numeric verification, and algebraic methods to automatically derive geometric theorems from diagram images.

Findings

Effective in generating nontrivial theorems from images

Demonstrates feasibility of automated geometric theorem discovery

Potential applications in education and knowledge management

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.