PreprintCC BY-NC-ND 4.0arXiv
Discovering Heron's Triangle Area Formula in a Morning in the Rain
Abstract
Motivations and derivations for Heron's triangle area formula abound. But how would one \emph{discover} the formula? We recount the challenge of designing a laboratory experiment to discover Heron's formula, and of doing so in the morning, in time for a noon class---a snapshot of collaboration with AI in fall 2025. We then reflect on extensions and generalizations.
Related
- Rigidity of projective area widths and a weighted Crofton formula on RP3
- From morning departures to evening returns: a probabilistic model for forecasting bike-sharing demand
- Discovering like a scientist: Literature-informed dimensionless learning for physical closure of data-driven equations
- Experimental Mathematics: Discovering The Half-Derivative from First Principles
- Valeur exacte de la mesure de Hausdorff d'un sous-ensemble fractal de dimension log 3 / log 4 du triangle de Sierpinski
BibTeX
@misc{grinberg2026discovering,
title = {{Discovering Heron's Triangle Area Formula in a Morning in the Rain}},
author = {Eric L. Grinberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22320},
eprint = {2609.22320},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22320},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Discovering Heron's Triangle Area Formula in a Morning in the Rain
AU - Eric L. Grinberg
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.22320
UR - https://arxiv.org/abs/2609.22320
AB - Motivations and derivations for Heron's triangle area formula abound. But how would one \emph{discover} the formula? We recount the challenge of designing a laboratory experiment to discover Heron's formula, and of doing so in the morning, in time for a noon class---a snapshot of collaboration with AI in fall 2025. We then reflect on extensions and generalizations.
ER -