Random Triangle Geometry Dataset: Area-Perimeter Relations and Shape Efficiency

This dataset contains randomly generated triangles used in the computational study: "Computational Exploration of Triangle Geometry: Area–Perimeter Relations, Shape Efficiency, and Triangle Shape Space." Triangles were generated numerically using GPU-accelerated Python code. For each triangle, geometric properties including side lengths, perimeter, area, and normalized shape efficiency were computed. The dataset is intended to illustrate statistical properties of triangle geometry and the emergence of classical geometric constraints under large-scale random sampling. Columns included in the dataset: a — side length b — side length c — side length perimeter — sum of side lengths area — computed using Heron's formula shape_efficiency — normalized area metric The dataset accompanies the preprint describing the computational analysis of triangle geometry. The code used to generate the dataset is included for reproducibility.