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Optimizing Geometry Problem Sets for Skill Development

Published: September 2, 2025 | arXiv ID: 2509.02758v1

By: Michael Bouzinier, Sergey Trifonov

Potential Business Impact:

Helps computers teach geometry by solving problems.

Business Areas:
Geospatial Data and Analytics, Navigation and Mapping

This article describes an ontology and methodology for annotating and organizing Euclidean Geometry problems, developed in the early 1990s and implemented as a software tool. While the majority of this work -- including the ontology and solution graph paradigm -- was completed over thirty years ago, we argue that it has renewed relevance in the context of modern artificial intelligence. In particular, we explore the hypothesis that this established framework can facilitate automated solution validation and feedback when paired with contemporary large language models, thereby supporting teachers and self-learners in geometry education. We document the original architecture and its enduring value, and outline pathways for bridging historical educational resources with next-generation AI techniques.

Page Count
12 pages

Category
Mathematics:
History and Overview