Computational Exploration of Triangle Geometry: Area-Perimeter Relations, Shape Efficiency, and Triangle Shape Space
Abstract
This preprint presents a computational exploration of triangle geometry using large-scale random sampling. One million triangles are generated through GPU-accelerated numerical methods and analyzed in terms of area–perimeter relations, shape efficiency, and triangle shape space representations including Kendall’s shape sphere. The dataset and code used in this study are publicly available: Dataset DOI:https://doi.org/10.5281/zenodo.19033949
Fields of Study & Subjects
Mathematics and Applications
Point processes and geometric inequalities
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 15 March 2026
- Language
- EN
- Document type
- Preprint