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| Main Author: | |
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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2025
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.17170941 |
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Table of Contents:
- <p>This work presents a unified trigonometric framework for studying the geometry of regular polygons, referred to as the <em>Functional Law of Regular Polygons</em>. According to this principle, every geometric characteristic of a regular polygon—such as angles, side lengths, radii, areas, and special ratios—can be expressed as a function of either its number of sides (<em>m</em>) or its interior angle (<em>θ</em>).</p> <p>The paper systematically derives classical and novel formulas, showing how fundamental mathematical constants such as the golden ratio and π naturally emerge from polygonal geometry. In particular, it provides new infinite series representations of π using methods of polygonal exhaustion inspired by Archimedes.</p> <p>Beyond its theoretical significance, the framework highlights deep interconnections between elementary trigonometry, geometric properties, and mathematical constants. It also offers practical and pedagogical value for computational mathematics, computer graphics, and mathematical education by providing recursive structures and infinite series for exploration.</p>