Symbolic Constructions & Demos¶
100% Exact SymPy & ``geometor.model`` Demonstrations Bringing Hero of Alexandria’s Geometry Alive
While the 4-Track Book Codex (Hero of Alexandria — Metrica, Definitiones, Catoptrica & Dioptra) preserves strict separation of historical text and scholarly commentary (zero embedded Python scripts), this Constructive Laboratory pairs every major theorem of Hero of Alexandria with executable, zero-float geometor.model DAG constructions, Rational Trigonometry invariants, and standalone Rich CLI demonstrations in demos/.
Walkthrough Page |
CLI Script & Core Builder |
Exact Algebraic Domain & Theorem |
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\(\mathbb{Q}\) on \((13, 14, 15) \implies \Delta = 84\), cyclic quad \(CHBL\), Quadrea \(\mathcal{A} = 16\Delta^2\) |
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\(\mathbb{Q}\) & \(\mathbb{Q}(\sqrt{5})\) on \((7, 8, 9) \implies \sqrt{720} = 12\sqrt{5}\), \(x_1 = \frac{161}{6}, x_2 = \frac{51841}{1932}\) |
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\(\mathbb{Q}(\sqrt{2}, \sqrt{5})\) Shortest-Path Unfolding \((|\Gamma E|+|E\Delta|)^2 = 162 < 180\) |
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\(\mathbb{Q}(\sqrt{3})\) Mean-Proportional Cut \(Q(A, D) = \frac{507}{4}\) & \(\sqrt[3]{100} \approx 4\frac{9}{14}\) |
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\(\mathbb{Q}(\phi)\) Universal Gnomon (\(\phi^2 = \frac{3+\sqrt{5}}{2}\)) & Geodetic Tunnel \((12, 5) \to 13\) |
Running All Demonstrations Locally¶
Inside the GEOMETOR Python 3.13 environment:
/home/phi/PROJECTS/geometor/.venv/bin/python demos/heron_formula_proof.py
/home/phi/PROJECTS/geometor/.venv/bin/python demos/sqrt_720_iteration.py
/home/phi/PROJECTS/geometor/.venv/bin/python demos/catoptrica_shortest_path.py
/home/phi/PROJECTS/geometor/.venv/bin/python demos/area_division_book_iii.py
/home/phi/PROJECTS/geometor/.venv/bin/python demos/golden_gnomon.py