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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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
LibraryPress@UF
2024-05-01
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| Series: | Proceedings of the International Florida Artificial Intelligence Research Society Conference |
| Subjects: | |
| Online Access: | https://journals.flvc.org/FLAIRS/article/view/135297 |
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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. |
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| ISSN: | 2334-0754 2334-0762 |