@article{Henning_King_Ngo_Shore_Gardner_Alvin_Stadnyk_2024, title={Lattice-Based Generation of Euclidean Geometry Figures}, volume={37}, url={https://journals.flvc.org/FLAIRS/article/view/135297}, DOI={10.32473/flairs.37.1.135297}, abstractNote={<p>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.</p>}, number={1}, journal={The International FLAIRS Conference Proceedings}, author={Henning, Jonathan and King, Hanna and Ngo, Sophie and Shore, Jake and Gardner, Alex and Alvin, Chris and Stadnyk, Grace}, year={2024}, month={May} }