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| 1. Verfasser: | |
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| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2025
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| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.5281/zenodo.17699285 |
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Inhaltsangabe:
- <div>When one lists the continued fractions of √ n across the natural numbers, a striking regularity appears: the coefficients rise in discrete steps, forming an arithmetical and visual staircase. This article reveals the algebraic and geometric underpinnings of that pattern. Each segment between consecutive perfect squares yields a constant pair of leading coefficients and a linearly increasing remainder, giving rise to a simple integer structure that unites the periodicity of quadratic irrationals with an illuminating global picture. We include a short proof of the fundamental relation and three complementary visualizations, along with a brief note on the golden ratio as a conceptual ”zeroth stair.</div>