TY - JOUR
AU - Henning, Jonathan
AU - King, Hanna
AU - Ngo, Sophie
AU - Shore, Jake
AU - Gardner, Alex
AU - Alvin, Chris
AU - Stadnyk, Grace
PY - 2024/05/13
Y2 - 2024/08/14
TI - Lattice-Based Generation of Euclidean Geometry Figures
JF - The International FLAIRS Conference Proceedings
JA - FLAIRS
VL - 37
IS - 1
SE - Main Track Proceedings
DO - 10.32473/flairs.37.1.135297
UR - https://journals.flvc.org/FLAIRS/article/view/135297
SP -
AB - <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>
ER -