Euclidean Geometry Ontology Catalogs (Facts, Objects, and Methods)

Annotation vocabularies of an ontology for Euclidean geometry problems and their solutions: 230 geometric facts, 143 geometric objects, and 97 solution methods, in English and Russian, with English–Russian translation tables and a worked solution-graph example (Figure 1 of the accompanying article). The ontology was developed in 1991–1996 by R.K. Gordin, M. Bouzinier, S. Trifonov, and I.F. Sharygin, and has been used since to annotate thousands of geometry problems — most of them publicly accessible at zadachi.mccme.ru — in support of curriculum design and granular skill tracking. It is documented in the article An Ontology-Based Approach to Optimizing Geometry Problem Sets for Skill Development (arXiv:2509.02758, submitted to the International Journal of Mathematical Education in Science and Technology), for which this record is the supporting dataset. Catalog content is licensed under CC BY 4.0; any source code in the repository is licensed under MIT.