Lattice-Based Generation of Euclidean Geometry Figures


  • Jonathan Henning Clemson University
  • Hanna King Furman University
  • Sophie Ngo Furman University
  • Jake Shore Furman University
  • Alex Gardner Furman University
  • Chris Alvin Furman University
  • Grace Stadnyk Furman University



Synthesis, Figure Generation, Euclidean Geometry, Textbook Problems, Lattice


We present a user-guided method to generate geometry figures appropriate for high school Euclidean geometry courses: a useful starting point for an intelligent tutoring system to provide meaningful, realistic figures for study. We first establish that a two-dimensional geometry figure can be represented abstractly using a complete, lattice we call a geometry figure lattice (GFL). As input, we take a user-defined vector of primitive geometry shapes and convert each into a GFL. We then exhaustively combine each these ‘primitive’ GFLs into a set of complex GFLs using a process we call gluing. We mitigate redundancy in GFLs by introducing a polynomial-time algorithm for determining if two GFLs are isomorphic. These lattices act as a template for the second step: instantiating GFLs into a sequence of concrete geometry figures. To identify figures that are structurally similar to textbook problems, we use a discriminator model trained on a corpus of textbook geometry figures.




How to Cite

Henning, J., King, H., Ngo, S., Shore, J., Gardner, A., Alvin, C., & Stadnyk, G. (2024). Lattice-Based Generation of Euclidean Geometry Figures. The International FLAIRS Conference Proceedings, 37(1).