| _version_ | 1866901059292626944 |
|---|---|
| author | Hanuschik, Michael |
| author_facet | Hanuschik, Michael |
| contents | <p>The Wallis product formula (1656) computes π as an infinite product whose denominators are 4n²−1. We show that these denominators are identically the twin spine visitor sequence of the Apollonian gasket with seed [−1, 2, 2, 3]. The proof uses only the Descartes Circle Theorem, Apollonian recursion, and elementary algebra. The gasket derives π from pure integer recursion. Exact, not approximate. This result is one consequence of Point-Sphere Theory (PST), a broader framework that derives fundamental constants of physics from the same geometric structure.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18791849 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Pi Derived: The Wallis Product from the Apollonian Gasket Hanuschik, Michael <p>The Wallis product formula (1656) computes π as an infinite product whose denominators are 4n²−1. We show that these denominators are identically the twin spine visitor sequence of the Apollonian gasket with seed [−1, 2, 2, 3]. The proof uses only the Descartes Circle Theorem, Apollonian recursion, and elementary algebra. The gasket derives π from pure integer recursion. Exact, not approximate. This result is one consequence of Point-Sphere Theory (PST), a broader framework that derives fundamental constants of physics from the same geometric structure.</p> |
| title | Pi Derived: The Wallis Product from the Apollonian Gasket |
| url | https://doi.org/10.5281/zenodo.18791849 |