Lattice-Based Generation of Euclidean Geometry Figures

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 represe...

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Bibliographic Details
Published in:Proceedings of the International Florida Artificial Intelligence Research Society Conference Vol. 37
Main Authors: Jonathan Henning, Hanna King, Sophie Ngo, Jake Shore, Alex Gardner, Chris Alvin, Grace Stadnyk
Format: Journal Article
Language:English
Published: LibraryPress@UF 13.05.2024
Subjects:
euclidean geometry
figure generation
lattice
synthesis
textbook problems
ISSN:2334-0754, 2334-0762
Online Access:Get full text
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Summary: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.
ISSN:2334-0754
2334-0762
DOI:10.32473/flairs.37.1.135297